"Just to be clear, how do you define hostile speech? It's not just 'speech when you're angry and want everyone else to know it'."
That's an excellent question, and not easy to answer; I'll do the best I can.
I use the term "hostile language" as a cover term to replace terms like "verbal abuse" and "verbal violence" and "abusive language" for just one reason -- because the other terms presuppose that the speaker/writer/signer has a deliberate intention to do harm, and I don't believe that presupposition is accurate.
My position on this is that although there certainly are people who use hostile language with the goal of doing harm and causing pain, they are in the minority. I believe that most people who use hostile language fall into these four categories:
1. Those who don't realize that any there's any other way to handle disagreement and conflict. Usually this is because they've grown up in a language environment where the response to any disagreement, no matter how trivial, is always hostile language.
2. Those who use hostile language to satisfy a personal need for excitement; they enjoy verbal fights for the "rush" they provide.
3. Those who use hostile language to satisfy their personal need for human attention. They've learned that hostile language does reliably get other people's attention, and they rely on it for that purpose.
4. Those who use hostile language and are genuinely unaware that it will be perceived as hostile.
In all four of those groups, even when the speaker/writer/signer does realize that the target may be hurt by the hostile language, causing that hurt is a side effect, not a goal. In all four of those groups -- especially Group #2 -- the speaker/writer/signer may not be angry at all. In all four of those groups, the speaker/writer/signer may be angry with someone other than the target, or may be angry about some issue that the target is in no way responsible for or involved in.
I define "hostile language" as language that a native speaker of that language will perceive as carrying an emotional message of hostility, based on that native speaker's intuitions. This is of course an entirely subjective judgment. Because there is still no recognized scientific mechanism for measuring and verifying the degree of hostility in a given sequence of language, subjective judgment -- unsatisfactory and inadequate though it may be -- is the only kind we have available right now.