Hey Brother... comin' from a place of love... It's kinda not cool to be all "Honestly, you should be ashamed."
I get what you're trying to convey. But, for example, a better way to convey it might be something like "You should really re-consider your stance on <??>, and here's why...." then say the other stuff.
Cause the moment you say a sentence like you did there, BOOM, immediately the discourse becomes adversarial, a me vs you thing, and mentally the other guy stonewalls, and ain't a damn thing you're gonna say after that is gonna actually penetrate and take root in the other persons mind if you lead-in with an aggro phrasing like that. Kinda of a "You can catch more flies with Honey, than you can with Vinegar" type of deal. Hell, just ask any (successfully) Married man, they'll tell ya how (un) well that works.
Yeah... call em out in public. But don't start off with trying to "embarrass" them. I mean think about it. You ain't trying to embarrass him. The end result is trying to get the guy to see the erroneous logic they displayed and the evident truth in what you are then presenting to them.
Even Better? Try writing a sentence that starts off with something like "Wait...I'm confused about something, can you Help me here?" and then say something like "I thought that <state your point>. Am I wrong here?" It immediately sorta takes the blame-game off the other guy in a clever way. All the while bringing to light the folly in their assertion. But you're not putting 'em on the spot like that. You're shifting the spotlight over to yourself. So they're a bazillion times more mentally receptive to what you're sayin'.
Try it sometime. It really works! Not at all saying I consistently employ these tricks... but.. I learned a lot of em off the former President of the company, who was a Grand-Wizard at Schmoozing! Like he had it down to an Art Form. And they really do work.
It's the same reason why people like self-deprecating humor. Do you really think the comedian is or does all those dumb things they are saying? No. It's just a clever way to bring those observations to light.... get the other guy to think about em.... without it being confrontational. Win-Win.