I would also like people to stop acting like feminism is egalitarianism when the label is clearly gendered.

Agreed.

Anyways, I'm aware that the usage of "man" and "woman" in leftist culture solidified rather quickly and unexpectedly into something that seems counterintuitive from an outside perspective, because I had an outside perspective when it happened. But I assure you, the difference in meaning to its older usage is both necessary and not actually hard to understand if someone takes the time to explain it.

Basically, the idea of sex (physical traits) and gender (mental traits) being distinct things became necessary as the need to refer to nontraditional combinations of them became a thing. Intersex people may have physical traits of both sexes, but have a clear gender. Transgender people are an obvious catalyst, having a gender that differs from their sex (post-operation, you could in theory use the word transsexual, but this has bad connotations from its history so it's not used). Some historical cultures have been argued to have more than two distinct genders, while obviously still only having two primary sexes. You can see how this gets a bit complicated and necessitates the differentiation of the physical and mental traits into different words. So, sex became the physical traits, and gender became the mental ones. Or maybe that was always the technical definitions, and they became more common in their usage. Either way, I hope you get what I'm saying. There are definitions for both terms, and more importantly, there's a need for the terms to be different and more technical than they are in common usage, when discussing sex/gender issues. This naturally bled into common usage as those issues became more culturally relevant, at which point they came into contact with "normal" people who were like "What? Why?" I'm asking you to keep an open mind about learning why, because it wasn't done for no reason. Apologies for the wall of text, it's 2:30am for me.