You are entitled to your opinions and if someone does you horribly wrong, it's okay to hate them. But if someone points their gun and you...
The trouble with that is when someone labels some completely justifiable venting as “hate”.
I have moments where I say “I hate men”. I don’t instantly mean that I want every last male-identifying person to have never existed (which is the true and ultimate definition of hate BTW). Of course not.
It’s a crude and brusque shorthand. “I hate X” generally means “This particular group of people have hurt me too often today and I don’t want to know any of them right at this moment.” Except when it’s used by people in positions of power.
Because people with the power will use it to make certain that large volumes of X will vanish off the face of the earth. And they’ll get away with it because that’s what power is.
“Hate won’t stop hate” is a slogan used most often by people in the white, cishet, able male category like -to use your example- a man with a gun drawn telling an anti-violence protester to put down the placard or he’ll shoot again.
Life as we know it is not an even playing field.
That’s why I don’t like “hate won’t stop hate”.
I’d rather say, “I understand you’re hurt, how can I help?” It’s less catchy, but it’s better for all humans.