I think it's missing the point to say that the problem with "believe women when they say things are sexist" is that you want to hear an argument that shows that something is sexist. There's this sense that if there are good reasons to think that something is sexist, then most people will be easily convinced.
Like, this post, for example:
Not at all... I think both genders are equally likely to bring their emotions into their assessment of something as bigoted.
The idea that I should just reflexively accept a woman's view of something as sexist is ridiculous. I tend to hold everyone to the same standard, which is that a gut reaction has value, but not as much value as being able to back it up with good reasoning.
So the first sentence is just a silly false equivalency. History makes it really, really clear that we're very vulnerable, as a society, to erring on the side of discounting some marginalized group's claims that things are tilted against them. We all agree that men were much, much more likely than women to be wrong on the issue of basically every women's rights issue from more than about 30 years ago. We all agree that white people were much, much more likely to be wrong on civil rights than black people. Most everyone here agrees that straight people were and are much, much more likely than gay people to be wrong on gay rights issues. One group's emotions tend to lead them to want to preserve their privileged position in society, and one group's tend to motivate them to seek justice.
The last sentence reads like a total failure of introspection. The ability of people to "hold everyone to the same standard" is exactly what's in question. Your ability to judge "good reasoning" is being called into question, when your judgment is that women are going wrong when they judge that something is sexist.
I mean, fundamentally, when two people are disagreeing about something, if they want to continue to disagree they've each got to have a theory of how the other is going wrong. A really bad theory, in almost everyone's case, is "I'm just smarter than everyone else and my judgments about what's reasonable are much more reliable than this idiot's". But at the same time this is a
very popular theory. Just like everyone thinks that they're better-than-average drivers, everyone thinks that they're better-than-average thinkers. This is a big problem. It's an especially big problem in cases like this, though, because an outside observer has a lot of reason to think that members of one group are going to be systematically going wrong for reasons that are invisible to them.
A problem is that a lot of people lack a good understanding of how bigotry works. Probably the way it's conflated with hate doesn't help. People look inside themselves, don't see anything that looks to them like bias, and then set themselves up as arbiters of what's reasonable. Like here, where there seems to be this expectation that if someone is being reasonable then they surely ought to be able to convince the speaker of that. But, really, this attitude, coming from someone in this position, seems like strong evidence that the speaker is unreasonable and is determined to remain so, since this has basically never been true in the history of bigotry.