“Putting Women Against Other Women”

The first part "Why are you trying to pit women against each other?" can be the Complex Question Fallacy (A question that has a presupposition built in, which implies something but protects the one asking the question from accusations of false claims.)

The second part "You should support other women" also has an assumption built in... that expressing disagreement is antithetical to showing support. This is a real problem today, since respectable discourse is the foundation of a strong society (or at least pretty damn important). It is also an opinion with which many disagree. When it comes to two individuals making claims, the claims that should be supported are those best supported by the evidence, regardless of the gender/race/intellect/identity, etc of the person making those claims.