Yes. This can happen when the person you're talking to is in the right but is being arrogant/obnoxious/smug about it. Publicly agreeing would be rewarding rudeness. I don't think that's even such a bad thing; they might only be right once, but they'll probably be rude forever, so why ever give them the satisfaction?
Effective arguing doesn't have to look like "arguing". You have to leave people an off-ramp so they can change their minds without feeling like they are losing a status contest.
Most people are emotional, not rational. Even people who are supposed to be rational are rarely unemotional about their beliefs.
It's why facts and evidence are so unpersuasive. If you don't make them emotionally and personally relatable most of the population won't understand what you're trying to say.
Which is why the rule is "People won't remember what you said, but they'll remember how you made them feel."
Effective arguing doesn't have to look like "arguing". You have to leave people an off-ramp so they can change their minds without feeling like they are losing a status contest.