Yes, I will call it a myth. Yes, women do start the divorce process, but the question is why.
This here is a stereotypical case.
If you scroll the social media, you will read vile and ugly comments from men about women. The comments are rooted in the apparent belief that women are gold-diggers and women mindlessly file for divorce.
However, if you read this link, you will see that the husband not only left, but he also went public with another partner. This is not uncommon and sometimes they move from the marital home into the "girlfriend's" home and tell the children the girlfriend's children are their new siblings.
I say that in these cases what women do is clean the mess that men have created by creating a new "family" while legally married to someone else. Since women are the filers or the "cleaner uppers", their name is the first on the divorce papers so statistically they are the ones who start the divorce and are therefore villainized. However, they are not villains just "cleaner uppers" and appropriately dealing with the situation.