Please bear with me in this answer as it needs a longer introduction in order to understand properly the main issue regarding your question.
In most cases, people who study Buddhism and interpret it in a secular way (by denying rebirth) are incapable of adopting the Buddha's middle way - they must (unknowingly) either side to one extreme ("self exists") or to the other extreme ("self does not exist") (which is in fact same as the first extreme ('self exists'), because there is a self who denies the existence of self).
The avoiding of extremes regarding self ("self exists" or "self does not exist") is clearly stated in this sutta:
"As he attends inappropriately in this way, one of six kinds of view
arises in him: The view I have a self arises in him as true &
established, or the view I have no self... or the view It is precisely
by means of self that I perceive self... or the view It is precisely
by means of self that I perceive not-self... or the view It is
precisely by means of not-self that I perceive self arises in him as
true & established, or else he has a view like this: This very self of
mine — the knower that is sensitive here & there to the ripening of
good & bad actions — is the self of mine that is constant,
everlasting, eternal, not subject to change, and will stay just as it
is for eternity. This is called a thicket of views, a wilderness of
views, a contortion of views, a writhing of views, a fetter of views.
Bound by a fetter of views, the uninstructed run-of-the-mill person is
not freed from birth, aging, & death, from sorrow, lamentation, pain,
distress, & despair. He is not freed, I tell you, from suffering &
stress.
Source: http://www.accesstoinsight.org/tipitaka/mn/mn.002.than.html
Siding to one of these two extremes ("self exists" and/or "self does not exist") is not in accordance to the Dhamma and is an indication of a wounded self (suffering).
(Please read until the end as it will become clear to you why I'm writing all this)
When self is wounded and this wound can't be healed by eradicating ignorance (with realization of anatta), there are only two options to ease this suffering:
- Kill the wounded self by rejecting its existence (altruism) ("self does not exist")
- Make the wounded self grandiose by decorating it (narcissism) ("self exists")
The above is nicely described by the Buddha:
"There are these two extremes that are not to be indulged in by one
who has gone forth. Which two? That which is devoted to sensual
pleasure with reference to sensual objects: base, vulgar, common,
ignoble, unprofitable; and that which is devoted to self-affliction:
painful, ignoble, unprofitable. Avoiding both of these extremes, the
middle way realized by the Tathagata — producing vision, producing
knowledge — leads to calm, to direct knowledge, to self-awakening, to
Unbinding."
Source: http://www.accesstoinsight.org/tipitaka/sn/sn56/sn56.011.than.html
In the above sutta, "That which is devoted to sensual pleasure with reference to sensual objects" is indulgence in desire which is typical narcissistic behavior and "that which is devoted to self-affliction" is self-mortification or the lack of appetites or desires by self-denial or self-discipline as an aspect of religious devotion which is typical for altruistic behavior.
Thus, the more the self is wounded (the bigger the suffering), the more he/she is an altruist or narcissist. Both altruist and narcissist suffer (have a wounded self) and the more they suffer, the more they make others suffer (altruist gives to others so much that others can't learn how to be responsible for their own suffering; narcissist takes from others so much that others suffer too much to learn how to be responsible for their own suffering).
An altruist who kills his/her wounded self and enters a spiritual path, usually believes in "rebirth but rejects its cessation", because he/she hopes for a better self in the next life ... actually, this next life is heaven, which is eternal life without suffering. Such person is more inclined to follow a religion and scorn Buddhist views. For an altruist religion can make perfect sense.
On the other hand, a narcissist who makes his/her wounded self grandiose and enters a spiritual path, usually believes in "no rebirth", because his/her self is so grandiose that it transcends EVERYTHING. In essence, his/her self is so grandiose that it becomes (a fabricated) Nibanna. He/she does not hope for the next life, because he/she is too perfect for it, that's why he/she rejects it. Such person is more inclined to follow Buddhism and scorn religious views. For a narcissist Buddhism can make perfect sense.
This fabricated Nibanna with which the narcissist's wounded self is decorated is so grandiose that is reachable only to the narcissist. It's for those reasons, that he/she has the belief "after death suffering ceases for all beings, no matter if ignorant or enlightened", because if it were otherwise, it would mean his grandiose self (fabricated Nibanna) is nothing special because it would be attainable to everybody after death. That's why he/she has the view that Nibanna is only meant for this one and only life (for HIM) and that after death there is actually "nothing"/"cessation of everything"/"void"/"emptiness". In reality, being ignorant and having such wrong views, he/she destines himself to a veryyyyyy long suffering in this very same "voidness". In reality, his/her wounded self is this very same "voidness", but he/she is denying it by projecting a fabricated Nibanna onto it. It's because of these very same reasons that he/she is destining him/herself to "(eternal) voidness".
Here comes the answer to your question ...
The more a person is a narcissist, the more that person distorts reality. Remember, he/she has no other choice ... his/her self is so much wounded, that he/she needs to fabricate a distorted self and decorate it in order to hide the wounded self. His/her distorted self can become so much decorated that in order for reality to conform with his/her decorated self, he/she needs to change reality itself. That's why he/she distorts reality and fabricates lies about reality. That's why he/she makes others believe in his/her lies. By making others believe in his/her lies, his/her wounded self is protected, because when others believe in his/her lies that is proof for him/her that his/her grandiose (decorated) self exists and that reality conforms with his/her grandiose (decorated) self. If someone sees through his/her mask (decorated self) and sees his/her lies, his/her wounded self becomes exposed to him/her, because when someone sees his/her lies, that is proof for him/her that reality does not conform with his/her grandiose (decorated) self, thus he/she sees his/her distorted (decorated) self is a fabrication and his/her wounded self becomes exposed. Because the wounded self is so much in pain, it is easier for him/her to deny the truth and fabricate new lies and make others who exposed him/her liars.
They are masters in presenting an obvious lie as being the truth. They have been doing this since childhood. They are masters in projecting their (fake) reality onto others. They are delusional, but they make you think that you are the one who is delusional. They are very intelligent and clever. They make you think they are enlightened and know it all, and that you just can't understand what they know. When asked a question, they don't answer it, but provide ambiguous and complicated explanations or "proofs", so:
- that you yourself can interpret the answer in the way that fits your
own views or
- the answer is just too complicated for you to understand
(sarcastically: because you don't have the Buddha knowledge, as they
do) and you let it go without bothering to ask for clarifications or
- the clever and confident tone of the answer makes you feel like you're too stupid
to comprehend it and you, too ashamed to admit that you don't
understand it, fabricate a lie to yourself that you actually do
understand it, following by you giving praise to the narcissist for his elaborate knowledge.
Hopefully, the Pali Canon is vast enough, so it's easy to see through this facade of lies.
So, what would be the secular interpretation for the Assu Sutta and the Mata Sutta?
You already know the answer. Just use your imagination. Remember, the interpretation given is delusional, but it seems legit, because he/she distorts reality in order to conform it with his/her "good looking self" which is just a mask for his/her "wounded self". The more the wounded self hurts, the more the interpretation will be delusional, or out of place, or just too complicated to comprehend for us poor mundane beings.
An uninstructed mind, not very well versed in the Dhamma, can quickly fall for such elaborate lies.
But an instructed mind, with an open mind, can't fall for it and will see through the lies by looking at the whole picture, not merely at the details that the narcissist points to. That's his/her game: he/she doesn't want you to see the whole picture, because if you see it, his/her mask would fall.
So, what would be the secular interpretation for the Assu Sutta and the Mata Sutta?
I'll try to answer this question. Thinking about it, it's not an easy task, but I'll try:
"Transmigration" is just a word given for arising and passing of
mental states in this one and only life.
"a being" or "being" is just a word given to a mental state where
there is grasping on the "I".
"father", "mother", "sister", "son" are merely a mind
state with grasping to the "I".
"water in the four great oceans" is just a metaphor used to deliver
the message how big is the suffering in this one and only life.
I'll add some more, which I found and can be related to other suttas:
"Birth is suffering" is interpreted as giving birth to children in
this one and only life.
"Physical birth" and "physical death" is just a
mental state with grasping to the "I".
When Buddha mentions the word "birth" he is really thinking about the
arising of a mental state with attachment to the "I" in this one and
only life.
When Buddha mentions the word "death" he is really thinking about the
ceasing of a mental state with attachment to the "I" in this one and
only life.
When the Buddha talks about eternalism and nihilism he is not
relating eternalism and nihilism to life after death, but merely to
forms of grasping to the "I" in this one and only life.
Nibanna means that suffering stops in this one and only life. Nibanna
is meant just in the here & now, for this one life.
"heaven" and "hell" are just descriptions of mental states of mind in
this one and only life.
When Buddha talks about "descending of consciousness into the
mother's womb", he does not talk about the consciousness of the baby,
but the consciousness of mother perceiving (hence "descending") she
is pregnant.
"Realms" refer to different states of mind in people in this one and
only life, where 'heaven' is pleasure, human is wisdom, animal is
instinctual behavior, ghost is craving and addiction and hell is
suffering.
"ending of rebirth" refers to ending of the arising of unpleasant
mental states in this very same and only life.
Side note: Did you catch it? For them everything is a "mind state" ... nothing is real. The mundane truth is not real. They deny materialism. In fact, they are denying this very same existence. That's why this is nihilism and has nothing to do with real Buddhism. Denial of existence is so typical of narcissists. This very same denial is actually making them materialistic (carnal). Furthermore, the existence of their very same grandiose self is making them materialistic (carnal). Because of lack of insight due to a strong sense of self they can't see this. They actually think they are in conformation with the Dhamma, neither nihilists nor existentialists, etc. and they fully believe it as the truth. Off course they will deny my claims by using distortion and prove that, actually, it's me who is materialistic, a nihilist, a liar, Mara, religious, a Christian, delusional, etc. ... but that would merely be their projection of their own issues (strong belief in non existence of rebirth, which is actually coming from their grandiose sense of self which is actually coming from a wounded self) onto me. They are masters of distorting reality by making the victim look like the abuser.
To be a radical secular buddhist you have to deny existence by claiming that it's just a mind state or, if you are really clever, deny existence by claiming that existence is Nibanna. Off course this Nibanna that you claim must not be anatta, but atta - your grandiose narcissistic self ... but your listeners would think that you're talking about anatta, so no worries ... you made a big enough distortion so that you feel important, which is better than feeling ugly, like your wounded self. Jokes aside, such denials of existence stem from narcissistic wounds inflicted upon the person in his/her childhood.
When a sutta is in contradiction to the narcissists grandiose views, they deny the sutta, distort it by cleverly twisting it and interpret it in such a manner to conform to their grandiose views of self which is some kind of (fake) Nibanna. If any sutta is too difficult for twisting, they use denial and distortion by raising issues with the authenticity of the sutta.
Looking at secular Buddhism in this way, it's clearly evident that secular Buddhism is really a kind of religion, no different than Christianity or any other religion, because both religion and secular Buddhism stem from self-views.
Off course there are other secular Buddhists who are less extreme and more open minded than presented here in this answer. Don't get me wrong, all of us have narcissistic wounds and use different methods to ease this suffering. The bigger the wound, the more grandiose can our wounded self become. By believing in no post-mortem rebirth, we actually prolong the healing process of this wound, that's why secular Buddhism is not the best solution. The best solution is to let go of all views as it was originally taught by the Buddha.
I hope you now see the truth behind it all.
Please note, I'm not an advocate of believing in rebirth nor rejecting rebirth nor do I think negatively about secular Buddhists or secular Buddhism. Everyone has wounds and uses whatever works to feel better. There's nothing wrong in it. With metta