There is no asymmetry because the word 'dukkha' in the context of the Three Characteristics (tri-lakkhana) does not mean 'suffering'; just as the word 'dukkha' in the context of feelings (vedana) does not mean 'suffering'. 'Dukkha' only means 'suffering' in the context of the Four Noble Truths.
'Dukkha' in the context of the Three Characteristics means 'unsatisfactoriness'; namely, the inability of impermanent (conditioned) things to bring permanent lasting true happiness. (Only the unconditioned Nibbana can bring true lasting happiness). Thus, the teachings state:
yadaniccaṃ taṃ dukkhaṃ, yaṃ dukkhaṃ tadanattā
That which is impermanent is unsatisfactory; that which is unsatisfactory is
not-self.
SN 22.15
In the Pali, many words, such as 'dukkha', 'dhamma', 'nirodha' & 'sankhara' have different meanings in different contexts thus, in each different context, must be translated differently & appropriately.
The Buddha was fully enlightened thus perfectly coherent. There can be no contradictions in a Buddha's teachings. It is the famous translators & gurus who are misinterpreting the teachings.
In summary, as shown in the quotes below, only the ‘dukkha’ of attachment & egoism is real ‘suffering’ (mental torment/trauma). The ‘unsatisfactoriness' of conditioned things (dukkha lakkhana) and painful feelings (dukkha vedana) are not suffering (unless they are attached to).
Context 1 - Dukkha as suffering
In summary, (all) suffering is clinging to the five aggregates (as
‘I’, ‘me’ & ‘mine’).
1st noble truth
~~~
‘I am’ is a construing. ‘I am this’ is a construing. ‘I shall be’ is a
construing. ‘I shall not be’… is a construing. Construing is a
disease, construing is a cancer, construing is an arrow. By going
beyond all construing, he is said to be a sage at peace.
MN 140
~~
He is seized with the idea that ‘I am form’ or ‘Form is mine.’ As he
is seized with these ideas, his form changes & alters, and he falls
into sorrow, lamentation, pain, distress & despair over its change &
alteration.
SN 22.1
~~
By & large, Kaccayana, this world is in bondage to attachments,
clingings & biases. But one such as this does not get involved with or
cling to these attachments, clingings, fixations of awareness, biases
or obsessions; nor is he resolved on ‘my self.’ He has no uncertainty
or doubt that just suffering, when arising, is arising; suffering,
when passing away, is passing away.
SN 12.15
Contex 2 - Dukkha as pain
Here a bhikkhu is an arahant, one whose taints are destroyed, the holy
life fulfilled, who has done what had to be done, laid down the
burden, attained the goal, destroyed the fetters of being, completely
released through final knowledge. However, his five sense faculties
remain unimpaired, by which he still experiences what is agreeable and
disagreeable and feels pleasure and pain. It is the extinction of
attachment, hate, and delusion in him that is called the
Nibbana-element …
Iti 44
~~~
When the Blessed One had entered upon the rainy season, there arose in
him a severe illness, and sharp and deadly pains came upon him. And
the Blessed One endured them mindfully, clearly comprehending and
unperturbed.
DN 16
Context 3 - Dukkha as unsatisfactoriness
“What do you think of this, O monks? Is form permanent or
impermanent?”
“Impermanent, O Lord.”
“Now, that which is impermanent, is it unsatisfactory or
satisfactory?”
“Unsatisfactory, O Lord.”
“Now, that which is impermanent, unsatisfactory, subject to change, is
it proper to regard that as: ‘This is mine, this I am, this is my
self’?”
“Indeed, not that, O Lord.”
SN 22.59
~~~
Then, friend Yamaka, how would you answer if you are thus asked: A
monk, a worthy one, with no more mental effluents: what is he on the
break-up of the body, after death?
Thus asked, I would answer, ‘Form is impermanent… Feeling… Perception…
Fabrications… Consciousness is impermanent. That which is impermanent
is unsatisfactory. That which is unsatisfactory has ceased and gone to
its end.
Very good, my friend Yamaka. Very good.
SN 22.85
Dukkha - contexts 3 & 1
All conditioned things are unsatisfactory — when one sees this with
wisdom, one turns away from suffering. This is the path to
purification.
Dhammapada 278
Contexts 1, 1 & 2, 1 & 1 and 1 & 3
Tisso imā āvuso dukkhatā, dukkhadukkhatā saṅkhāradukkhatā vipariṇāmadukkhatā.
There are these three kinds of suffering, my friend: suffering due
to/about pain; suffering due to/of mental concocting; and suffering
due to/about change.
SN 38.14
Note: That 'attachment is dukkha' is an ultimate truth because every experience of suffering is bound up in attachment.