There is one other possibility that no one seems willing to concede to:
That Carol Marcus may well conceive Jim Kirk's child, not only without his concent, but without so much as his participation. She could impregnate herself with some of his DNA. I know that she's not a biologist or physician, but she is a scientist, nonetheless. As far as what her motivations for doing this might be, they could well come from a failed romance with Kirk and wanting some part of him with her ... forever and always. It might have nothing more to do with the fact than that she's, quite simply, always wanted a child - but not necessarily a husband. Carol's already noticed Kirk's attributes, which she finds terribly attractive. Who else to procreate with but the crème de la crème of STARFLEET?