My wife never really learned that, she'd give him boobs and he'd feed/sleep. That worked perfectly for the first six-ten months, and then it didn't.
I'd never had those to fall back on, and was always the one who took over when he was being "difficult". Then again I was also the one that pushed him in his pram for a walk around the block at 2AM, in sub-zero temperatures, to help him fall back to sleep. They were hell on my sleeping patterns, but also some of the best early memories I have. Talking and singing as the snow fell .. magical.
Sometimes when I returned my wife told me she couldn't sleep cause she missed him. I guess they just where very close. Sometimes I envied that - now that he is bigger we have a lot father- son activities, so that makes up for that.
Men and women are just different parents and I believe kids need both parts or even more. Grandparents and aunts and cousins, friends and teachers. The kids are always happier in a crowd that just with one parent or even both parents. Nowadays everyone threats parenting as a two person job but everyone will agree the saying that it takes a village to raise a child...
Breastfeeding is another example of why it is more "natural" for mothers to stay home than fathers, though.
At this stage the bond between them both is so thick, that they are basically inseparable. As man you basically spend a whole year to catch up.
So even with enough money and leeway from my employer to take parental leave there are still issues why childcare is mainly the part of the mothers. I guess most of the feminists don't have children. Oh and try to have two children. Guess what: it does not scale well! And it takes more than two persons to even raise one child. I would encourage you all to try it yourself. It is really rewarding to be a parent and also so exhausting - even with all the privileges in the world.