Whoa, asking me to make sense? Your mileage may vary! But what I'm trying to say, is that once people are married and produce children, the main thing they're going to do of lasting value is to parent those children. Parents will be held responsible for what the children do, legally for many years, and to some extent eternally. (If you're not a Christian, disregard that last bit - the concept works on a secular level, too.)
So what's your Real Life? Is it your job? If so, the concept of "paternity leave" makes sense - a little break to play Daddy, just like you'd take a little break to go skiing. But if you define yourself first as a husband (you married her, after all!) and then as a father (you were there, too ...) then it's almost like you're taking "leave" from fatherhood to go be a (doctor, lawyer, engineer, Indian chief).
Did that clarify, or muddle further? The point is what you, I, anybody, think their life is really ABOUT.
Well, it just seems to me obvious that BOTH parents play an important role in a child's early development. As I understand it, you acknowledge the important role to be played by the mother and have no objection to her taking leave from her employment for some period of time. (You know, at one time, the pregnant mother just moved to the perimeter of the field that she had been working and had her baby - lol.) But it sounds to me as if you have come to the conclusion that the father's role is not sufficiently important to justify his taking leave from work.
What factors did you weigh in coming to that conclusion?