There's Buddhist doctrine on that subject in the Bhikkhuni Sutta (AN 4.159):
'This body, sister, comes into being through food. And yet it is by relying on food that food is to be abandoned.' Thus was it said. And in reference to what was it said? There is the case, sister, where a monk, considering it thoughtfully, takes food — not playfully, nor for intoxication, nor for putting on bulk, nor for beautification — but simply for the survival & continuance of this body, for ending its afflictions, for the support of the holy life, [thinking,] 'Thus will I destroy old feelings [of hunger] and not create new feelings [from overeating]. I will maintain myself, be blameless, & live in comfort.' Then he eventually abandons food, having relied on food. 'This body, sister, comes into being through food. And yet it is by relying on food that food is to be abandoned.' Thus was it said, and in reference to this was it said.
... and ...
This body comes into being through sexual intercourse. Sexual intercourse is to be abandoned. With regard to sexual intercourse, the Buddha declares the cutting off of the bridge.
In other words, food is one of the necessities or requisites of "the holy life" -- and sexual intercourse is not that kind of necessity.
See also the topic Why the Buddha abandoned asceticism which has more on the subject of not-eating.
i am trying to understand how "eventually" occurs
I think the Theravada doctrine is that enlightenment happens in stages -- see Four stages of enlightenment.
So the first stage is to be free of identity view, and to see the dhamma correctly, and so on.
The two stages after that are minimising and (eventually) being free of sensual desire and ill will.
And the last stage etc.
how "feelings destroy"
I'm not sure I understand this question of yours.
I think that the doctrine about "feelings" is summarised in the doctrine of the 12 nidanas, which is that feelings and delighting in feelings leads to craving (for the delightful feeling to continue or to reoccur), etc.
There's also doctrine related to the "three poisons" -- i.e. that pleasant feelings tend towards craving, unpleasant feelings aversion, and neutral feelings ignorance or confusion.
Hence the advice about food: don't abstain from eating in order to create a feeling of hunger, don't over-eat to create a feeling of overeating, just eat enough to remove the feeling of hunger -- the "middle way", neither one extreme nor the other.
if not "i" is there then "why need to support further 'i' by worldly activities & how does this happen"
You might want to read the various topics tagged suicide, I think they say that suicide is not the right way to liberation from egocentricity and self-view.
Read the four noble truths again:
- death is painful, birth is painful, etc.
- suffering is caused by craving -- which includes the craving for becoming, also the craving for cessation
I think that Buddhist doctrine says that human life is rare and valuable -- a rare opportunity to meet and understand and practice the dhamma, and to thus experience liberation and unbinding -- which is not the same as the wheel of life, the cycle of death and birth.
2nd para & your conclusion:: i nowhere asked for "sexual intercourse"
Well it's the definition of adultery
voluntary sexual intercourse between a married person and a person who is not their spouse
Perhaps you said "adultery" as a metaphor or something, not meant literally. Even so, if the advice about intercourse isn't relevant to your question, then the advice about food might be.
Also if your thoughts about "the body" (e.g. cellular division) is causing thoughts to tend toward suicide, SN 54.9 might be relevant -- the Buddha set a group of monks to meditate with "foulness of the body" as a meditation subject, after/during which some monks killed themselves ... after which the Buddha taught a different kind of meditation, related to breathing ("anapanasati").
I think that the "meditation on the foulness of the body" type of meditation is recommended only for people who have a trouble with lust, i.e. as an antidote to sexual desire or desire for adultery -- and isn't meant to suggest that suicide is the correct solution.