One thing that helps: remember that there are many people reading your response, one of them possibly being the person you replied to. Write for the audience, not specifically for the person you're responding to. It's a rare thing for someone to change their mind; it's a much more common thing for others to read your comment and gain something from it.

I just wanted to tell you that I read your comment immediately after writing mine and it's almost eerie how similar they are. There's the proof, if we needed any!