Literary textual analysis is not seen as a particularly credible method for deducing facts around here.

My argument doesn't rest on the claim that literary textual analysis is a credible method for deducing facts. It rests of the claim that feminists use literary textual analysis as a method for deducing facts.

It rests on the claim that the fact that feminists find their facts that way is one of the main reasons for the conflict between feminists and evolutionary psychology.

Your problem is that you can't distinguish a descriptive statement about the truth that some people use literary textual analysis to find facts from a value judgement about whether it's good that they do.