Okay, so. For several years now I've had a habit of inserting myself into arguments my family members have, trying to resolve things and get people to do what they're supposed to. I try to help parent my little sister when mom is busy. I try to defend my brother in conversations he's having with mom. And try to defend mom in conversations with dad. And try to defuse conflicts between my brother and sister. And... mom wants me to stop doing that. All of it. Like this morning I was trying to explain why my brother did X and didn't do Y like she told him to, and she's wanting me to stop. And I'm not my sisters parent so I shouldn't act like it. But... how do I stop doing this, exactly? My immediate thought when she asked me to stop was "but what am I supposed to do?" And I don't know if I understand the answer. How do I "stay out of it"?
I think some of it depends on where the line is? Like, there's nothing wrong with keeping an eye on your little sister or helping her with stuff, but yeah, you shouldn't be parenting her. And yeah, your brother can make his own explanations. It sounds a lot like in general you're trying to minimize conflict, so if being around conflict distresses you, leaving the room to go read a book or something could be one thing to do. I think having something to redirect your behavior instead of trying to stop cold turkey would probably work best - especially since removing yourself from a situation means that you'll have less opportunity to intervene.
Not sure how to help, but I wanted to mention that I have had similar problems when my parents argue. Like, I can see the problem, I want to help fix the problem, and it upsets me that I can't, but it upsets them more when I try to mix in. So, just saying you're not alone, I guess.
Remind yourself that your parents are grown adults who can handle their emotions (and could handle them long before you came along). It's hard, but there's not much more that you can do except repeating to yourself that you're not responsible for controlling their emotions and actions, and making the conscious decision to resist the urge to intervene. It gets easier with time, but it starts like this. Walk out of the room, feel bad, survive the feeling-bad, and the next time you do it you'll feel less bad, and eventually you'll come to actually believe that nothing good comes out of intervening and that you deserve to take care of yourself first.