By your reasoning, one could equally support a law giving fathers sole custody of children under age 6, and resist any change in that law because, as you reason, mothers could use that change as a tool in divorce litigation. Presently, how many fathers put up with a crappy marriage until the child is 6 so they will have some parental rights? How many mothers threaten divorce with children under 6 in order to manipulate their husbands?
In Qatar, Kerry seeks to convince Gulf Arabs on Iran deal (Reuters)
from the article: An eyeful of mothers