Mothers are more committed to children than fathers because of their initial investment: the egg
Each individual wants as many surviving children as possible. The less he or she is obliged to invest in any one of those children, the more children he or she can have.
The obvious way to achieve this desirable state of affairs is to induce your sexual partner to invest more than his or her fair share of resources in each child, leaving you free to have other children with other partners.
This would be a desirable strategy for either sex, but it is more difficult for the female to achieve. Since she starts by investing more than the male, in the form of her large, food-rich egg, a mother is already at the moment of conception ‘committed’ to each child more deeply than the father is. She stands to lose more if the child dies than the father does.
More to the point, she would have to invest more than the father in the future in order to bring a new substitute child up to the same level of development.
If she tried the tactic of leaving the father holding the baby, while she went off with another male, the father might, at relatively small cost to himself, retaliate by abandoning the baby too.
Therefore, at least in the early stages of child development, if any abandoning is going to be done, it is likely to be the father who abandons the mother rather than the other way around.
Similarly, females can be expected to invest more in children than males, not only at the outset, but throughout development.
So, in mammals for example, it is the female who incubates the foetus in her own body, the female who makes the milk to suckle it when it is born, the female who bears the brunt of the load of bringing it up and protecting it.
The female sex is exploited, and the fundamental evolutionary basis for the exploitation is the fact that eggs are larger than sperms.