“Woman” vs “Female”

Here’s something I saw on twitter this morning:

That prompted a question from me:

I suspect that “Woman Trouble” (meaning, difficulties someone is having with a female romantic partner) and “Female Trouble” (meaning, ailments for which one might seek aid from a gynecologist) are both fairly problematic phrases, and I never use either.  In fact, I can’t think of anyone I know who uses them, except ironically and in the company of people who get the joke.  (And I know some people whose speech habits are pretty thoroughly untouched by feminism.)  That one has “woman” and the other has “female” doesn’t seem to matter much.

Anyway, poster Kait the Great then put up this clarification, perhaps not in response to me specifically:

Though I do still wonder about my original question.  Phrases like “Female Trouble” vs “Woman Trouble,” whatever else may be wrong with them, don’t suggest that “woman” and “female” are interchangeable.  If the problem with, say, “woman driver” as opposed to “female driver” comes from such a suggestion, then that might explain why “Female Trouble” and “Woman Trouble” are equally awkward.