Why are they doing more harm than good? Because, after a claim like that, the conversation is over. There's absolutely no point in talking to someone who makes claims like that. And it makes you less likely to be willing to talk to the next person, either. So the net amount of whites willing to learn and talk about race and racism goes down when people say stuff like this.
(It's also factually untrue, blatantly unfair, and bigoted...)