Arguments should work out like this:
Person 1 and Person 2 disagree on a topic. They both explain why they disagree, citing various pieces of evidence to support their positions. If the argument remains peaceful, one person either changes their mind on the topic or the two people agree to disagree.
If not, there's always the chance for drama. Just don't burn bridges. Apologies are good ways of smoothing over past nastiness.
If that fails, there's always muting.