It's a desire to pass on their own genetics. It is a biological desire we dudes feel. Because reproduction in caveman times was essentially a contest of who was best and the best got to reproduce, you can see this in other social animals like wolves and deer.
Single moms, especially ones with multiple children are much less likely to want any more kids and want to focus raising the kids they already have so basically the guy becomes a beta wolf who is raising the pack alpha's pups because he wasnt deemed good enough to mate. It feels even worse when the ex husband is a real POS so theres this underlying feeling of supporting the genes of an outright inferior male. This is all under the surface instincts that manifest as feelings we guys cant really explain. Well adjusted dudes can get over this as mating has come a long way since caveman days and passing on ones genetics is no longer this do or die scenario.
That explains genetics obsessed incels like Lucas. Ones like Chris is more about wanting to return to the mindset of childhood but being unable to reverse time. The only way they can think to recapture this is by assuming one of the other roles in their idealized image of a family, namely the father, so they can relive their own childhood experiences through their offspring. Almost everone with kids does this to some extent, it just gets creepy about how obsessed some dudes get about it and it becomes an indicator of a problem.