Reminds me of the Principle of charity [1] that "requires interpreting a speaker's statements in the most rational way possible and, in the case of any argument, considering its best, strongest possible interpretation".
I've found adopting this mindset to be one of the most important habits I've picked up, and eliminates so much drama.
This is also the basis of the Steel Man Argument [0] [1], as opposed to Straw-manning. Instead of attacking (basically nitpicking) the easy missteps in your opponent's reasoning, find the best form of their argument, and then argue with this. It seems to me as the ideal way to both win over those on the other side and provide yourself with a solid ground. You present yourself as avoiding undermining their position (really listening and caring to understand where they are coming from) and present a better argument yourself.
I’m not interested in telling you you’re wrong. You being wrong is your problem. I’m interested in my being right. If I can extract some information from our conversation that moves me to a better understanding of things then I have done all right from the interaction (assuming the time involved is short). The steel man allows me to extract this information from the interaction.
In practice, if someone isn’t capable of using the information I provide to re-assess their position, continued interaction is likely to be low quality. This isn’t a fault thing. It could just be that I’m incapable of interacting reasonably with this person. Either way, it’s then time to disengage.
Obviously it depends on the circumstance, but not every disagreement is about "winning" the debate. Sometimes the win is in building or saving the relationship.
Steelmanning is just applying the Least Convenient Possible World principle to debating. If you're picking nonessential nits then you might technically be right but you're probably also dodging the actual interesting questions.
This is in fact the only way to maintain credibility with both sides when resolving an argument. Unfortunately judges who routinely follow this rule are uncommon.
Paraphrased as the (oft-ignored) third guideline for HN comments: "Please respond to the strongest plausible interpretation of what someone says, not a weaker one that's easier to criticize. Assume good faith."
I've found adopting this mindset to be one of the most important habits I've picked up, and eliminates so much drama.
[1] https://en.wikipedia.org/wiki/Principle_of_charity