The main issue isn't "Who is more disadvantaged?"

We can bring up each issue separately and address multiple things at a time.

For example rape is a problem, and so are false rape claims. Let's address each separately. It is fallacious to say "My issue is more important, so we should ignore yours."

This is where some people have issues with Feminism or Men's Rights. If Pat says, "We have to address false rape claims," and Sam replies, "Rape is the real problem," that is a fallacy.

If a Pat says, "We have to address false rape claims," and Sam's response is, "You're ignoring rape," that is a bad argument. Pat is addressing a single issue, and now Sam is reframing the argument to a different issue. If Pat said, "We have to address false rape claims, and rape isn't an issue anymore," then Sam would be correct with the original response.

This is another way to describe the problem:

A correlative conjunction is a relationship between two statements where one must be false and the other true. In formal logic this is known as the exclusive or relationship; traditionally, terms between which this relationship exists have been called contradictories.