Nonetheless, in the case of babies, my personal feeling is that a mother is more (feeling for words ...) immediately essential. Not that babies aren't mad about their fathers, not that fathers don't derive great and lasting benefits from caring for their babies ... I never feel better about my husband, than when he's with our babies.
But men don't experience pregnancy, childbirth, or the care of an infant quite the way women to. For example, I had a miscarriage last month, at 5 weeks. Having guessed I was pregnant for only three weeks, I'd already "discerned" the baby's sex, named him, planned what he would wear home from the hospital, posed for pictures, imagined the early weeks of nursing him ... my husband, although he was saddened that we wouldn't be having the baby we expected, had not experienced the "relationship" I had.
There's a physical sense of motherhood, particularly of a young infant, that is not as typical of fatherhood. Now I'm not nearly as cool a parent when the kids get older ... "Oh no, we're stuck with Mama? Clean the house and take naps!"
As always, opinions are significantly conditioned by experience. My father was a Navy officer, and was gone up to a year at a time when I was a child. My husband's work has often involved considerable travel. (We all hate it - I really wanted to move to the farm and raise goats!) I may incorrectly diminish the necessity of fathers because of the periodic absence of fathers in my life, and my children's lives.