Dear {Name},
I regret our argument. I know we didn't see eye-to-eye on the movie, but I never should have dug in the way I did. Of course, our friendship is more important to me than some Hollywood fiction.
I haven't changed my mind on {element}, but I do see your point regarding {element}. I was thinking, though, that because things got so heated, maybe next time we should {choose a different activity/change genres/etc.}.
I'm sorry again for playing movie critic and letting my stubbornness ruin an otherwise fun evening.
Sincerely,
{Name}
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