I agree with this. A woman has to recover after giving birth to a baby. On top of that, she can breastfeed her child while a man cannot do that. Sure, a mother can put some of her breastmilk in a bottle and the father can feed her milk to the baby, but the most natural and simplest thing is for the mother to feed the baby directly.

On top of all that, the baby was inside the mother for 9 months. He's still going to need her for the first few months of his life so he can re-adjust to life outside the womb. It's important that the father begins holding the child and bonding with him, but the baby was never inside of his father, just half of him was, so the baby is simply not as familiar with his dad as he is with his mam.

Dad staying at home with the kids is still a valid option. But it should be a backup plan rather than the first plan.