and why was she wearing a TKD black belt in a karate class?
You get people who think they are greater than they are, you get boasters, it's life. It's not a gender issue but one of someone thinking they are something they'd aren't or are actually far less self confident than they want you to think, again not a gender thing. Actually the OP made a point of telling us that he wasn't a beginner actually though he was a white belt in karate, and had lots of experience so........
There's always the issue of course of how hard is too hard, one person's hard maybe another's well that wasn't very hard! Again though the OP made a point of matching her 'hardness', why? Would it have been difficult to say look let's calm this down a bit or would that seem like giving in to a woman? if a white belt is sparring a black belt, regardless of gender one goes at the pace and force that a white belt can take, not too easy but just enough to challenge the white belt. The black belt has more experience, more control. If they are coming on too hard then stop you don't escalate it.
I also bet I've sparred with more men who go harder than women, I've sparred with more men than women for whom sparring with women is a problem for their egos, this is in karate and grappling.