Your analysis is woefully inadequate. First the most obvious point: many women are single mothers but not divorced. They're (vainly) hoping their spouse will return some day. Or they're poor and so are their husbands. They can't afford to hire a lawyer, and there's nothing to get even if they do. 

The number is almost 70%, not 70-80%. But then you have to ask the reason WHY more women initiate divorce proceedings. The lead author in the study that discovered that fact, Michael Rosenfeld, suggested that women may be more likely to initiate divorces because married women reported lower levels of relationship quality than married men. That in turn contrasts to the fact that relationship break-ups of unmarried couples are initiated equally across genders.  

Before you take the step of rubbing a woman's nose in something, maybe you should reflect on that typically male habit and why you feel the need to use it.