if you're going to nurse the baby, (breastfeed) I agree with him.
When my first son was born, my husband did get up at first part of the time to help with the baby.
Soon it became apparent that it was a waste of time.
#1 I woke up instantly whenever the baby cried. I then had to wake him up.
#2 after he went and got the baby, I would be reawakened to feed him. You can't breastfeed while asleep, not at first anyway.
I finally decided it was not worth it to wake HIM up every time the baby woke me up. And so yes, he did better at his job, which was putting food on the table.

and yes, premarital counseling sounds like a good idea for you guys if you are already arguing about unborn children.