In a traditional U.S. marriage of a hundred years ago, the husband worked, the wife stayed home and took care of the house and the children. The wife not only did not work, but did not have the job skills that would enable her to get work. Marriage was a bargain that not only would the couple be monogamous, but also that the husband would support the family financially for life. The breakup of a marriage freed the husband and wife from living together and allowed them to find other mates, but did not free the husband of his duty to provide for the family.
In the U.S., family law is state law, different in every state, and very complicated. When a couple divorces, the court has to look at everything about the marriage situation, and decide what is equitable based on the details of the particular case. Often, the decision involves alimony, child support, or both. Often, the alimony ends if the spouse remarries, and the child support ends when the children reach some particular age.
The general social bargain is that both parents are responsible for the children, and, depending on the situation--who keeps the kids, who keeps the house, how much money each partner earns--a judge might well decide that it is fair for one spouse to make payments to the other.