Short answer: it's complicated
Usually I would prefer sitting back and just let argument go on their own, unless the conversation gets to the point where either side points out something that's very obviously just incorrect (not necessarily when the person is being highly emotional).
It's like when you're seeing someone hitting the wall because they couldn't see the wall, except since this wall isn't visible and they might not realise they are hitting something, more often than not it would result into some very sad moments because people get way more offensive when they are told being wrong than when they are told hitting a wall, even though metathorically they are actually the same thing.
The other times where I'd (attempt to have a) debate is when there are some things where I want to understand more about, whether to gather more information or to act as a confirmation to my own thoughts because others seems to be too opposed to them to the point where self-doubt happens. This sounds cool and all but most people would just see debates as an opportinity to mess things up, whether it's with themselves (overwhelmed by logic) or with others (overwhelmed by emotions). And if they aren't interested in it they aren't even going to bother since "what if I said something wrong and this guy just jumps into what I said and make me/others unhappy?"
Debating is one of the few ways that gets me into talking with others because as socially withdrawn as I am I do like taking account in other's perspectices, but the tragedy is that it is a way that most people are opposed of because of the way it works with them.
So sometimes it's like, do I even care enough to engage anymore?
____________________