The scene in TWOK shows that Neither recognize each other initially. Kirk definitely doesn't recognize David. If he'd ever seen David, it's been so long ago that Kirk had to ask if he was David.
Well, probably the last time Kirk saw him he was a kid; the NEXT time Kirk saw him, he was coming after him with a knife. Not exactly the best circumstances for recognition.
David DOES seem to recognize Kirk; after his first (utterly spastic) attempt to jump him fails he squares off and mutters "You!"
Im gobsmacked at the number of people who do not understand why people are upset at Kirk being portrayed as an absentee father.
That's just it, he wasn't "absentee" at all, David knew who he was and Kirk knew who HE was. He had obviously been present at some point, just didn't raise him and wasn't involved in the family.
In either case, not sure how that makes a difference considering that this is a thing that happens often enough in real life, even more so in military families.
we are relating to this story in the context of our lives now and the reality is plenty of children have absentee parents and do not feel happy about that situation. In fact, they are painfully aware of the absence.
And then there are children who never notice the absence because their main parent makes sure their emotional, physical and psychological needs are fully met. And then there are parents whose absence is felt strongly even though they never actually go anywhere. All of these are various permutations of how families develop for real people.
David doesn't seem to have missed Kirk all that much, in fact his problem with Kirk seems to be by reputation rather than anything personal. On finding out that Kirk isn't the Good Soldier Flag Waving Prick he always assumed him to be, David basically apologizes to him for misjudging him. That's not the actions of somebody who has issues with being abandoned, that's the actions of a secure and well-adjusted person simply changing his mind about someone else.
The objection that Kirk respected Carol's wishes doesn't change the fact Kirk was an absentee parent.
To be sure, it's unlikely Kirk was ever actually a PARENT in that sense. Carol didn't want or need him to take responsibility for David and specifically told him not to.
More importantly, what was he supposed to do instead? Break into her house with a phaser and demand she let him take David on the Enterprise for years at a time? How exactly is that supposed to work?
Kirk could have fought to see David and be a part of his life. It is called being a father.
Well, no, that's called being an asshole. Insisting on having a presence in someone's life when your presence is neither wanted or needed, and when said presence is actually completely incompatible with the most fundamental facts of your existence. Kirk's career would have taken him into deep space for years at a time where the only contact he would have with David would be a few subspace messages and an occasional visit every couple of years when the Enterprise happened to be on Earth. AND you're suggesting that Kirk specifically disobey Carol's wishes -- her, the parent who is actually raising him and responsible for him on a day to day basis and is the only full time parent he has -- to force a relationship he is in no position to invest in and cannot actually benefit either of them? I'm afraid not; Kirk's only possible reason for forcing that situation would be to give the appearance of "owning his responsibilities" and reconciling his own conscience, which would still fail to meet David and Carol's needs and would accomplish nothing except to soothe his own ego.