So you’re talking about your trans male friend, and out of your mouth slips the dreaded “she”.
This is how you ought to respond: “Crap. Sorry. He.” And then continue.
This is how you definitely should not respond: “Oh my god! I’m so sorry! I promise I see you as a man, I really do! I’m trying so hard, it’s just that I knew you so long as a girl, but I know you’re a man. I’m so sorry. I didn’t mean to, it was a complete accident. Please forgive me. I’m not transphobic or anything, it was a slip of the tongue…” and so on and so forth for fifteen minutes.
I can already see the people going down to the comment section to opine that people do the ten-minute apology thing because they are afraid of the evil trans cabal. But in my experience that’s not true. It’s usually because people understand that misgendering hurts trans people and, because they are kind-hearted and compassionate, they don’t want to hurt anyone. Unfortunately, this particular method of showing that you don’t want to hurt anyone is kind of counterproductive.
First of all, in general, when you commit minor acts of rudeness, you should just apologize once and not fourteen times. I know this is hard for everyone– I myself have, after a significant amount of work, managed to lower my usual number of apologies for minor mistakes to three– but it generally makes people uncomfortable to have someone self-flagellate in front of them.
Second, there are two situations that could be happening here.
First, you really do instinctively see your trans male friend as a man, but you’re used to using female pronouns for him, or actually he’s nonbinary and you’re not quite comfortable with using ‘they’ for single people yet, or you just made a dumb mistake because people do that. (I once called my extremely cis boyfriend ‘she’.) In that case, you have nothing to apologize for, because you didn’t actually do anything wrong. Everyone misspeaks sometimes. It’s okay.
Second, you do not see your trans male friend as a man, you see him as a woman. That isn’t something to beat yourself up about, because most people cannot actually switch their instinctive gender categorizations of people. I have been around enough trans people that my gender classification system is fundamentally broken and now not only occasionally misgenders trans people but also parses a bunch of cis women as being men, which I suppose is equality of a sort.
But if your trans friend is socially dysphoric, the fact that you see him as a woman causes him a great deal of pain. Like I said, it’s not pain you can necessarily fix, so it’s not like you’re doing something wrong; this is just the unfortunate way social dysphoria works. However, the polite thing to do in this case is not to rub it in his face. That’s why trans people ask other people to use the right pronouns for us: we can’t reasonably ask everyone to see us as our gender, but we can ask people to refrain from making us constantly aware of the fact that they don’t.
The problem is that spending ten minutes apologizing about mispronouning someone is rubbing it in his face that you don’t see him as a man. Like, it’s literally a ten-minute conversation about the subject! The list of events most trans people would prefer to that conversation includes root canals, having a door slam repeatedly into their face, and being left in charge of a dozen sugar-high seven-year-olds at a Chuck E. Cheese’s. This is a pretty shitty way of showing your allyship.
It is okay if you struggle with guilt issues about having just mispronouned someone. I would suggest that the correct way to deal with these issues is not to continue to hurt the person you just hurt, but instead to talk to someone else. Or journal, or go for a run, or whatever your preferred form of self-care is.