Something to consider is that people can gloss over an explanation for convenience. For example: in the previous sentence, I didn't provide any proof that it's accurate. You could make the argument that nobody glosses over explanations for convenience.

I don't think it's necessarily worth proving every statement, because that'd be extremely time-consuming. But if you provide an opposing viewpoint, back it up with clear reasons (this helps filter out positions that are undefendable), and I'm interested in defending my position or continuing the discussion, then we can have a meaningful discussion from that.