I'm so sorry for the arrogance I displayed on {date}. I don't know why I get that way sometimes, although it does tend to happen when I especially want to engage with someone (and maybe impress them a little).
You deserve better than to be treated so condescendingly. While I know my presence must have been a truly insufferable affair, I really do offer my sincerest apologies. I hope I can make it up to you by taking you to coffee or something. I'd like to hear more of what you were saying about {subject}.
Sincerely,
{Name}
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