I'm not sure I understand that part. Could you flesh that out for me?
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.