You are missing the point by being too literal, too narrow. Of course hating a murderer does not turn the hater into a murderer. That's not the argument.
The thing we hate is evil, Occhi. Evil. What is wrong with murder? Theft? Rape? Bullying? Cheating? Lying? These are all manifestations of evil. So is the thirst for vengeance. That is a door that opens on darkness, which can consume and destroy.
There is an urge when dominated to fight back, to seek domination in turn. There is no balance to this, no correcting of the course, no justice. There is only payback.
That was the sentiment of Ozy's remark. I suggest that the costs paid are higher than advertised, while the return gained is markedly lower. Vengeance doesn't fix or heal anything. Good people will only feel remorse or emptiness after they exact vengeance. That is the temporary delve into the dark side, and it is pricey. Or... they will more permanently become the thing they hate, which is even costlier. Either way, the venture is tainted. The emotion, the temptation, will betray you. Vengeance is not worthwhile. It certainly isn't worth embracing systematically.