I am saying that their "but if a man did it" argument has at least 2 large plot holes.

Some groups have some explicable defensible necessity for the discrimination. People would indeed have a different opinion about a man violating his way into a group for women recovering from being violated by men. This mgaician group can not, or at least has not, produce any such justification of fundamentally unavoidable necessity.

And the group has to actually be merely a social club as they said. They used those words as part of their argument, so you can't consider any groups with any kind of material consequences when comparing "but what if a man did it". If a man is a knitter and there was agroup that billed itself as the worlds best knitters, that is a material consequence. There is a badge that is recognized as indicating the best, and they meet the standard, yet they can not have that badge that tells clients that they meet the standard. This group does appear to have that quality at least somewhat, and so is not just a "social club".

And so the argument is just gratifying garbage.

Then you're not acknowledging that a group for men that has a specific kind of power within a certain sphere that has excluded women is very different than a group for women in that same sphere. There is no uniform rule that can be applied, which is where you're getting tripped up. Uniform rules often favors control by those who have power.

I'd go with "you have never feared that you might be raped and killed while walking alone at night".