If you are going to argue with someone, you have to see them as rational; otherwise, arguing can’t reach them. You have to try to understand them on their own terms if you are going to give reasons that they see as reasons.
Arguments matter because we live an embedded life in which reality determines moral life, and moral life determines reality. In other words, is it not only true but also legitimate?
Let’s say you and a random social media user, disagree over abortion.... The answer to this question matters greatly. It’s not like a dispute over our particular tastes in food which can remain unresolved without jeopardizing our relationship – it must be settled.