YTA if your definition of "yelling" is actual yelling. Reprimanding is one thing but there is no need to get loud and start yelling at either if them. If your strategy of setting boundaries with your children is done by yelling at them then youre gonna have a lot of difficulty in the near and far future. There are better strategies to get your point across, set boundaries and expectations, and discipline your kids.

kids get lots of mixed messages when it comes to bullying. Every single story about heros, etc. theyre exposed to tells them "it's ok to hit someone if they're being mean to someone else. That makes you a hero."

You should talk to them about those messages and explain that those stories are fun but they don't actually reflect how we should behave in real life. We know Spiderman is a "good guy" because we witness all his motivations and all his actions but in real life, we only have a tiny glimpse as to why people do the things they do. When someone sees your kid hit another kid theyre going to assume that your kid is the bad guy in this situation because that's all they saw. Unfortunately, your kid can't really prove that he was defending his brother but it's also besides the point because his brothers life was not in danger and your kid could help the situation in other ways like letting you know about it so you can do something for his brother. That's the best thing he can do because then you can protect them both instead of him putting himself at risk by punching his brothers bully.

This will probably need to be repeated in different ways at different moments as they continue to gradually grasp all of the meaning behind all of this.

Remember, kids do not think like adults. They physically can't. They don't think rationally; they experiment and/or emulate behaviors. Yelling at your kids just teaches them how to yell. And they will eventually yell back at you resulting in shouting matches that go no where and instead deteriorate your relationship.

Think about when people yell at you. Did you ever want to listen to them or follow their "instructions"? No. You wanted them to stop yelling. Even if they "listen" to you in the moment they'll still do the behavior whenever they think they'll get away with it because they weren't actually taught why they shouldn't behave that way.