> Why is using "her" everywhere worse than using "him" everywhere?

Because its just as gendered and conflicts with standard usage (which, in English, accepts the use of the masculine linguistic gender for subjects of unknown sex or gender identity, so it is not better from either a "gender neutrality, regardless of accepted usage" standpoint or from a "clarity of communication through conforming to accepted usage" standpoint.)

Tell me, where did I say that? This behavior of yours (putting words in people's mouth and accusing or insinuating them of sexism/racism/elitism etc.) is exactly why this stupid "singular they" phenomenon has arisen.