Even worse than this, sometimes I find myself changing my mind internally but feeling compelled to defend my initial opinion, as if being convinced is having lost. That’s definitely detrimental to a conversation.
1. Leaving room for your debate partner to save face is about as important as crafting a convincing argument.
2. Become comfortable with the condition of your debate partner never explicitly conceding the argument.
3. Explicitly conceding points that you agree with helps the other person save face to do the same back.
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.
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."