Part of the reason I can never just intrinsically go along with someone going "well I used to lean left, but then once I actually started looking into things my attitude changed real quick" is, like... going somewhat centrist is one thing, but going full-on right? It immediately makes me think of something like:
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Well, "wage-gap" is deceptive. It's framed as if women are paid 21-30 cents less who are by all accounts, working the exact same as men. In the early years of its adaptation as an argument, it was conveniently ignored WHY it is what it is.
It's no less true, but instead of active malice, it's mostly systemic issues. Fewer women go into a certain subject, fewer women that do can actually make it, women work, on average billable hours(this one is important) less than men do, so of course they'll get paid less! They have less experience, they're working for the company less, and etc,
Now, for many people, it ends there, except, well, the why for those goes deeper into systemic social issues, too. WHY do women work less? Because they're the ones generally, socially, relegated to taking care of the kids that they are generally, socially expected to have. And from a young age, they are eased into careers that are "girly" as opposed to ones that aren't -- surprise surprise, they often pay less.
And we can get into whether or not a socialization-driven choice is actually freedom of choice or not(some people, predominantly the religious, believe that there's always a choice, even when there's only one choice), and whether or not we can, could, or should change it.
So one simple issue is actually much, much deeper than that, and the solution? Well, according to people who go as far as "women are paid less than men for the same work, 30 percent less!" it's to just pay women that entire difference more. But should we pay a woman who has two years of experience as much as a man with 10 years of experience, even though the woman lost out on 8 years of experience through no fault of her own?
Reducing these arguments to something that simple and then, when it's questioned, trotting out the justifications -- no matter how true they are -- for the argument, before, once we learn how outrageously unfair it'd be for anyone to fix it in a certain way (saying yes, we SHOULD pay the woman with two years experience the same as the guy who has 10 years), retreating to the original argument and saying "You just want to pay women less for the same work!" starts to get on peoples' nerves. It's a classic motte and bailey fallacy.
That's why it pisses people off. And once you do that once, now EVERYTHING looks like a motte and bailey fallacy, even when it's not. Then, the original problem (that gender roles relegate women to having less experience, fewer billable hours even when they do, or the notion that women shouldn't be aggressive, but sit there and look pretty) never gets fixed because people don't want to change and, even if they did, they don't want to go too far.
Now your entire movement looks wrong, and the opposite side looks better, even marginally, because at least they're not "hiding their true intentions." (Except they frequently are)
Everything goes to shit from there. Next thing you know, you're babbling about ethics in human resources and tipping a fedora. It's not pretty.
quick edit: Keep in mind that the argument I used there is exaggerated. Nobody is claiming women should get paid more for less work or less experienced work...except for people who are easy to frame as insane, and they are used as strawmen to bring people in the middle over to 'their side.' This was a common GG tactic mostly because actual insane people on both sides are usually the ones that end up actually arguing as opposed to discussing with each other, and that further brings more people into the same fold as t hose extreme outliers. Meanwhile, everyone else discussing gets to suffer the fallout from it.