You lost the thread of the conversation the moment someone confronted your belief that it doesn't have a clear definition.
The reason you lost the thread is because you're struggling with the internal contradiction of your belief.
Our carceral system is widely recognized to be deeply racist in practice and in philosophy. This being the case, it's not an unbelievable stretch to say that when someone holds a belief in capital punishment, there is a good chance they also have parallel beliefs that rationalize capital punishment as a functional part of that racist system.
In that case, such advocacy is part of their rhetorical framework of hate speech. The clarity of the definition of hate speech gives us to see the context of that.
Let's imagine you work at a social media company. You see the comment: "capital punishment should be legal". You don't know anything about the carceral system of the jurisdiction the commenter lives in.
Do you remove the comment for being hate speech, or not?
But the main point is that since the other commenter reached the conclusion that this would be hate speech, and you reached the conclusion that it might be but not necessarily, it follows that the definition he or she proposed is not clear.
I don't know how to make this any more explicit. Hate speech having a clear and defined concept (which both you and that other commenter can research on your own) gives us a way to define whether or not the comment and context is harmful or not. I'm not going to hold your hand here, you need to read about it.
I am not discussing whether or not hate speech is clearly defined. I was discussing whether "Speech that explicitly or direct line implicitly dehumanizes anyone" is a useful definition. Do you think that's a useful definition, or not?
If that wasn't the point you were arguing against, then we're going nowhere.