Maybe I'm not expressing myself well enough, but I'm not sure why you jumped from "telling someone they are wrong" to "antagonize and attack". I feel like you can almost always do the first without incurring in the second.

I 100% agree that if you tell people they are wrong aggressively and arrogantly, that will backfire, and they are probably justified in ignoring your correction.

But some people, and particularly some organizations, seem incapable of accepting even the most thoughtful correction, and that's the kind of place/people I'd rather keep a distance.