COST of a normal break up vs cost of a divorce.
There is a huge difference of financial outcomes of a break up between a 7 month relationship and a 7 year marriage.
For the 7 months relationship the couple moves on, and no financial re-arrangements happens. For the marriage, there is a much higher chance that the woman: 1) takes custody of the children (if the couple has them) 2) is recipient of child support 3) is recipient of alimony payments
You can say that a "divorce" is much more costly to men and hence they are more likeley to stick it out a relationship or try to make it work, but there is less cost to women (financially at least), hence they are more likely to initiate it.
Given the current marriage laws are a remnant of the 50s and 60s lifestyle (of women staying home, and needing financial protection in case of divorce), you can argue that the current law framework in the US encourages the initiation of the divorce from women, and discourages that from men.
Since no divorce costs are involved in a normal 7 months long relationship, you see men initiating breakups just as much as women.
TLDR: Current divorce laws favors women by a long shot, hence they are more likely to initiate it.