You have not disproved that the concepts are opposed in this instance. Which matters much more than whether or not "stereotypes might generally be true." Like, at best stereotypes are a distraction for the actual data we'd like to have discussions about.
> You have not disproved that the concepts are opposed in this instance.
Nor did I aim to. I only wanted to dispel the mistaken belief that stereotypes are mostly false in general. That you think I should have instead addressed some other point that in your opinion matter more is irrelevant - you are free to address it yourself.
The wider claim doesn't actually change anything about the discourse. You have not contributed to the discussion, because you've provided no additional information about whether or not the underlying claim is true. We are no closer to truth because of your comment. So you have not "dispelled the mistaken belief that stereotypes are mostly false in general" because we can't make an active assumption about this stereotype without directly proving it.
So... Their original point stands without direct evidence against it. As you have not provided direct evidence, your point is moot.