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.

[0] https://en.wikipedia.org/wiki/Straw_man#Steelmanning

[1] https://lifehacker.com/utilize-the-steel-man-tactic-to-argue...