Women do not think with their reproductive organs, that is the way men operate a lot of the time. A woman chooses a male because she is attracted to him/loves him, few women would choose a man on the basis of how good he is in the sack.
And women in Europe were also activist up to a point to get equal rights. In the US it is more conservative politicians who want to keep the good old times in place and women have to use political activism to get equal rights through the courts because the political reality in the US means that getting equal rights through the political process is next to impossible (in a timely fashion).
And when the marriage breaks up it is still the husband who has to provide money to the wife in order for her to care for his (and her) children. And that is mostly because in the US there is no financial safety net which women get part of the money from until the child is old enough to go to school full time (at which time the woman is to start working close to full time).
In the Netherlands men have to pay considerably less most of the time than in the US. In the US this leads to unfair judgments towards the men. Maybe it is time for US law to order women to start working as soon as the children are old enough to be in school full time. If the women are not trained enough the US states might provide loans in order for her to start learning a trade so that she can stop draining her husbands pocketbook.
And the reasons that it is much easier for women to break off the marriage is not the whole story, women usually see break ups as the last resort. Men don't want to divorce as long as they still have their sex, still have their laundry done and food on the table.