They don't hand out F-16s to everybody who signs up. There is a very strict method to qualify first as a pilot and then rate high enough to qualify for the single engine fighter. Even if they qualify, there is a rigorous training program in the F-16 before they are certified. So as a pilot she has to be good.
Being a good pilot and being able to work with people are two different things. There has to be more to this than they are telling.
I think you're missing the point.
More conservative types are supposed to get aggravated because she only got this slot because she is a she and because of her looks and women shouldn't be doing this sort of thing anyway.
More liberal types are supposed to get aggravated because they never gave the woman a chance, undermined her, and immediately rejected her to put a male in the position to perpetuate the patriarchy.
Tossing out some explanation that could just as easily apply to both men and women in any context where high skill and excellent leadership skills are required deprives both sides of the opportunity to get angry. We can't have that.