The reason they were irritated at her sarcasm is clearly motivated by sexism, there's absolutely no reason to deny that and I definitely never intended to, so I apologize. I see no reason to get super defensive here - I want people to actually understand what I meant.
Is the statement inherently wrong? No, but it’s also an inadequate response to harmful behavior.
Simply disagreeing with people who defend sexist rhetoric isn’t enough. It doesn’t get the job done, and at a certain point, silence may as well be complicity.