Not a double standard, because the situations are not symmetrical.
I wanted to admit that I, too, fail, and wrongly contextualize female-sourced sexism in a historical timeline of taking a lot of unfair shit from their culture, and give them a pass. But I shouldn't. It is no less wrong, and the victim is no less deserving of protection.
Laying out your initial logic, in order:
p1: A has power
p2: B has !power
p3: A exerts power
p4: B exerts !power
c: if p1 and p2, given p3 and p4: asymmetrical situation
Of course it is! And yet nothing is proven.
It sounds an awful lot like you're either intentionally or unwittingly advancing the logically and philosophically weak argument that [undesiredThing]ism = Prejudice + Power--formulated by Bidol, spread by Katz, cornerstone of Bell's Critical Race Theory, and subsumed by Crenshaw's middle-class-feminism+CRT intersectionality fusion--as if it is inherently true and proven. There are myriad problems with that equation.
This maxim has seen a surge in the last couple years as online blogging has massively repeated it ad infinitum. People encounter it and walk away, impressed that they just reduced [undesiredThing]ism to a neat equation proving racism/sexism/Xism only exists at the intersection of prejudice X and [some kind of problematically defined] power.
And yet this has been repeatedly and adequately contested, while the CRT/intersectionality adherents keep moving the goal posts from one form of power to another over the last few decades (they appear to have, for the time being, settled on institutional power).
Again, your logic, as offered (filling in the latent assumptions):
x: ethnic+sexual group
y: involuntary genetic membership in x
z: x historically exerted most institutional/structural power
p1: power is y + z
p2: if p1, sexism is prejudice/bigotry/discrimination against a person based on sex + offender possessing p1
p3: A committed action X against B because of B's gender
p4: B committed action X against A because of A's gender
c1: given p3 and p4, instance-level act is same
p5: if p1, and A has y + z, A has power
p6: if p1, and B has y + !z, B has !power
p7: 'structural level' sexism is caused/reinforced by p2
c2: if p2 and p5, given p3, A is guilty of p2
c3: if p2 and p6, given p4, B is not guilty of p2
c4: if p7, given c2, A causes/proves p7
Does that make things clearer? There are only about a half-dozen premises there that need actual proving.
Oh, also, fwiw, and I'm being pedantic here: saying sexism is sexism--especially after the lengths to which I've gone to actually define sexism--is in no way an equivocation. I do not use ambiguous language; nor do I prevaricate.
Your attempt at informal logic is also pretty laughable. I'll try to give a better response than this tomorrow though in another reply, as you seem to be actually engaging with this, which is actually super awesome (it also doesn't hurt that my degrees were in Logic, and I hardly ever get to bust that stuff out in forum comments).
I guess I shouldn't have bothered with the reply, as it appears to have triggered a pissing contest over Logic technicalities. Or perhaps you think a dispute on mechanics is going to erase the problems inherent in the idea that selective power assignments to individual agents based on uncontrolled genetic factors is required to determine whether or not an act of sexism is verifiable sexism.
The efforts to redefine sexism/racism/etc as power-dependent are philosophically problematic. I'm rather uncertain we'd get anywhere on the issue.
edit: Also you mischaracterise my entire point. Not surprising given your sloppy thinking. It isn't anything to do with 'whether an act of sexism is verifiable sexism'. It also isn't 'power dependent' - power is only an aspect or manifestation of structure that is easy to talk about. You'll note (if you can read) that in the post where I discuss power I have first an example of a simple non-symmetrical situation that is analogous to sexism (to do with exerting power), then I talk about sexism. I have nowhere said that institutional sexism is solely about power differentials or power relations.
You might find people more willing to engage in discussion if you didn't resort to abusive language in nearly every comment you've posted to HN.
However, I could be the one who is mistaken, so I will see if being more civil in future actually works, and somehow magically cures people of being sloppy thinkers, subliterate morons, shitheads or trolls.