I'm not trying to derail the discussion by pointless complaints about etymology, I'm saying that part of the problem with the concept of hate speech is that the name given to it obscures (accidentally) the nuances of how it is applied in practice.
A better analogy would be if the critics of homophobes genuinely thought that homophobia was literally a fear of homosexuals, causing the homophobes to complain that this framing of their position made it hard for them to explain their objection to homosexuality.
By hiding the subjectivity of "hate speech", people then get surprised or angry when it does or doesn't get applied to terms like "communist bandits" or "OK, boomer", or "eat the rich". The real debate isn't about whether the terms are hateful (as the name suggests), but whether the specific groups that are targeted need the specific protections being implemented.
