I also seem to have offended one person I know rather severely.

From this sentence I gather that you're concerned mainly with in-person arguments. My own experience is that I argue extensively on the internet, but I'm quiet and modest with my friends and family. Mostly I suppose I'm just not that assertive in person. But if I had what I'm gathering is your problem, I would basically: take care to watch the faces of friends and family (constantly, or at least whenever there's conversation). Think how you value your relationship. That's a lot of mental effort, but it should supply you with a ready, natural-feeling motive to tone down or end an argument.