This is very good manners and also the default in some cultures, a huge humiliation to do otherwise.
On the other hand you might have people, who will always argue against anY correction you have and correcting in private makes it seem for them, that the discussion is 50-50, that it is only you telling them something is wrong and their opinion is as good as yours. It might not be worth correcting, unless critical, in such cases though.
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This is very good manners and also the default in some cultures, a huge humiliation to do otherwise.
On the other hand you might have people, who will always argue against anY correction you have and correcting in private makes it seem for them, that the discussion is 50-50, that it is only you telling them something is wrong and their opinion is as good as yours. It might not be worth correcting, unless critical, in such cases though.