This is a very important question I wish more trans people would take seriously. "Transphobia" is simple and short enough to fit on a bumper sticker but doesn’t really answer the question. It’s also frequently wrong.
Trans haters don’t always suffer from an "irrational fear or hatred of trans people." They’re responding to the very real threat trans people pose to a worldview and societal organization grounded in a sex-gender binary. It’s one that says there are only two sexes, gender identity unfolds effortlessly and always consistently with a person’s biological sex, and gender presentation is reliable indicator of a person’s gender identity and biological sex. All these beliefs are proven fictitious by the very existence of transgender, genderqueer, and gender non-binary people.
Pulling the rug out from under an entire social and cultural edifice erected on a fictitious notion of sex and gender is the real threat (and real power) of transgender people. That’s why they’re feared and hated so much. Their existence is a truth that reveals society’s lies. And that’s just intolerable to some.