No apology needed! I've not previously considered this in the depth needed to answer your question. I've tried my best to think seriously about your question and represent my true opinion faithfully, which has been a valuable exercise. I regret I haven't made it shorter, but 4 hours is about all I can afford to spend.
> What is this desire, how does it feel? I've never felt it.
> Is it a thought process or do you feel it in your body? (like hunger, sexual attraction...).
I know I can't live forever (and I wouldn't want to - mortality gives us purpose), but I feel I (along with everyone else) am an important part of solving a set of problems (meaning of life, best state of humanity, etc.) that may take infinite (or all we have) time. My impact on the world can be extended (perhaps indefinitely, certainly for as long as I will be aware of it) through my offspring.
I'm not a religious man, but it's what I would consider a religious feeling. It's a feeling clearer to me, having had children, than it was before them. I'm not sure I would have appreciated it in my early 20's, but a had an inkling of it by my late 20's.
I am (half of) the link between my and my wife's ancestors and our descendants. I'm the only one who can fill that role. Acknowledging this gives me a place in a grand narrative and drives my responsibility to my children to prepare them to take their place in the chain (even if that place is a dead end), with all that entails. Ignoring it prunes my branch of the tree.
I do think sexual desire is a base-level, noisy (in the same way that not all stomach pangs are hunger), subconscious drive to reproduce. We (like all living organisms) are a tool DNA uses to reproduce, and it's good at getting us to do stuff. I'd like to think my rationalization based on ancestry isn't a post-hoc result of that drive, but I can't be sure.
> Do you feel pain in your body (chest pain, knot in the throat..) if you think you cannot fulfill that desire?
I'm usually a fairly unemotional guy, so I tend not to feel (or, at least, not to notice) such things. Considering the death of my children can evoke a physical response, but that's more concrete. I do feel joy that I have the opportunity to fulfill my desire, so it may also be my optimistic nature masking the potential of tragedy. Ultimately, if my children fail to carry on the line (due to death or lack of desire), I will have done my part as a link in the chain to the best of my ability. I can be happy with that.
> How do you feel if you think about the fact that when you are dead, it just doesn't matter if you passed your gene or not? Isn't that desire just a rationalization/mental process vanishing in oblivion?
My father died when I was a teen, leaving 4 children. It may not matter to him now, but to us and the lives we touch daily it matters a great deal that he passed his genes first.
Ultimately, I'm not passing my genes on for my benefit. I'm doing it for my progeny's benefit and for the benefit of the impact they can have on the world in my stead.
> Where does that desire goes if you scale-up the total human species life-span? Would you feel happy that you will have grand-grand-grand children that you will never meet?
Of course! I know who my great-great grandparents were, roughly what their lives were like and some of the hardships they had to overcome, and I'm glad they lived and procreated so I could too. I'm the product of an unbroken line of millions (billions, if you want to consider the full history of DNA) of years of ancestors. It's a privilege to be a link in that chain for my descendants as well, even if I never meet the vast majority of them.
> I've never felt the desire to pass my genes to anybody. I have sexual desire, does that mean I want to pass my genes? But I feel like, sexual desire is like taking a piss: I just release some build-up in my body. I cannot rationalize my peeing in: I have to pee, because that ensure my survival hence the succession of me gene. I feel the same of orgasm. It feels that thought process is forced and conditioned by society.
I've observed (and experienced) that many men need till their late 20's to be ready for a committed relationship, and that a stable relationship makes them ready for kids. YMMV. Not everyone wants kids, and that's fine. Not everyone that wants kids gets the opportunity. That's less fine, but life's a bitch sometimes.
There is undoubtedly a societal bias, but which way it pushes differs based on who you ask. I don't feel I was strongly affected either way, nor pressured by family, friends, or spouse; so I'm fairly sure I've avoided that bias in this response.