What makes it better? (Or either of them anything other than neutral, mundane words?)

"female" and "male" are very clinical, scientific terms. They also lack humanity - there are male and female dogs, cats and birds, but that's not the case for "men" or "women".

No, none of this is backed up by a dispassionate reading of a dictionary but that's language for you. It's emotive, for better or worse.

What makes it better? Well, "man" and "woman" are Anglo-Saxon terms, not Roman, so there's that...

But, in the main, it's just my experience that anybody insisting on using the terms "male(s)" or "female(s)", when it comes to people, is up to no good.

"Female" sounds like something police, Ferengi and incels say, so "woman" just sounds more pleasant.

That’s not an alternative when you want to leave age unspecified. Read the link and the clumsy “women and girls” construction, which the rabble rousers have scared everyone into using, even in medical contexts!

Context usually negates the need to talk about the adultness or humanness of certain subjects. If the whole population of America saw the headline "Two female programmers played a pivotal role...", absolutely zero people would be shocked to find out that the females were adults and not 5 year olds, or humans and not dolphins.

Indeed, which makes me wonder why everybody is so surprised to see the term "women".

Because 'women' is only a noun, and it is used as an adjective in the title.

You can gramatically say 'Two women played a pivotal role in the..." or you can say 'Two programmers played a pivotal role in the...", but you can't, at least to my ears, cleanly say 'Two women programmers played a pivotal role in the...'.

What sounds more correct to you?

"I saw two men teachers at the ceremony", or "I saw two male teachers at the ceremony"

I'm sure we can just use the former language to the point where people recognize both as equally correct, but as it stands currently, most English speakers would far prefer the latter over the former.