You know, both Nick Meyer and William Shatner have said repeatedly, particularly in their respective books, that the scene was re-shot, after studio prodding, to change Kirk's question to "why didn't you tell ME" so that Kirk doesn't look like a schmuck who ignored his own son all of his life. However, having watched TWOK a million times, I feel pretty confident that what's in the film is "why didn't you tell him."
Regardless, I don't think the whole "deadbeat dad" thing fits with Kirk's character. Yes, he's had a number of relationships with women, both serious and purely physical (though far less than the stereotype). However, Kirk is not an irresponsible person nor an immoral one. I can't see him willfully choosing to ignore his own son, regardless of the circumstances of his conception. That just doesn't play for me based on everything else we know of the character.