The culture war can only be won by rhetoric, and the best rhetoric leverages morality, not empirical data.

Aristotle noted that most men cannot be convinced by facts and reason (dialectic); they require emotional appeals, or rhetoric.

Vox Day has a good video about Rhetoric and Dialectic

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When it comes to rhetoric, I will make just two observations:
* The most effective rhetoric is grounded in truth and facts.
* The most effective rhetoric is grounded in appeals to morality.

Thus,

The most effective discourse against feminism will be simple, truthful, and leverage the dishonesty and immorality of feminists against them in an emotional way

That is what makes "man hating lesbians" so effective: true, simple, appeal to morality.

Mere factual debunking has some effect, but the moral component is indirect. It fails to distinguish between deliberately misleading lies, mere factual errors, and statistical misinterpretations.

Much better if you can expose knowing untruths used to manipulate.
It is much more effective to e.g. know about how feminists attacked Erin Pizzy, founder of the domestic violence shelter movement, for not lying about domestic violence being a man-on-women thing, than to just cite statistics. Highlighting their dishonesty and selfishness needs to be part of that mix.

Simplicity is required for effective rhetoric. Indirect, complex, cognitive appeals to morality will fail, as will anything else requiring logical though to unpack. This is why memes are so effective - simple, moral, truthful persuasion.

Just my two cents on how to win the debate.