You're perceived intention should be irrelevant during an argument. Either expose the belief directly so it can be engaged with honestly, or focus on the logic of the argument being made. It is entirely possible to be both correct in your argument and incorrect in the foundational belief. But engaging with a factually correct argument with the assumption that it was borne from a place of ignorance just makes YOU less capable of being reasonable.

The first poster made a claim, and assigned faulty logic as justification.

The second poster pointed out the flaw in this logic.

The third poster ignored the logic argument entirely and resorted to an appeal to outrage rather than the structure of the argument itself.

Personal experience, beliefs, gender, identity. All of these points are entirely irrelevant to the argument at hand. The title of this post was about logic. The second commenter pointed out a legitimate logical error, and the third commenter exposed themselves at appealing to indignation and dressing it up as an argument. You (royal you) shouldn't support bad reasoning just because it agrees with you.