The thing about Robin being bullied that people don't get is that he can't just "leave". He can't just "snap" and abandon the team. It's shown multiple times in the series that he's the most willing to keep the team together, and that when they do split, he has nowhere to go.
The Hive? he would rather be homeless than going there. Being fr he has never shown any like for them in the series. Yes, they would treat him well, but only if he behaved. And we know he won't. He's way too controlling and Gizmo will never give him the leader role. Maybe he could co-lead, but he would miss the Titans, and ultimately leaving the Hive too in hope of getting them back together. He's shown to be very determined about keeping the team together, so it wouldn't be a surprise if he did this. But again, we are in a weird scenario where he, for some reason, decided to try being in The Hive, which wouldn't happen realistically.
The Titans East? Same as before, but even worse, ironically. He has a bad relationship with 4 of the team's members. He pretended to be Menos and treated him considerably worse than Mas in "Mas Y Menos", he also pretended to be Speedy, kidnapped him and fought with him just because of jealousy. And well we don't even have to say much about Kid Flash. Yes ik, BirdFlash is fun sometimes, but Rob wouldn't last a single day in the same house as this guy and would constantly fight for the leadership. All of this combined makes it a terrible place for Robin to be at. He would just go from a stressful place to another. And we're saying this without considering if they would even allow him in the team. Which... with everything mentioned previously, there's no way they let him in. If anything I see Bumblebee being kinder to him and providing help, maybe convincing her team to let him in, but it wouldn't last more than a week (and knowing the show's humor, no more than a day).
"Well he can slways go back to Batman right?" Yeahhhhh no. Robin is not only terrified of Batman (as seen in "Sidekick" and "Thanksgiving"), but also dispises him for making him live in his shadow, and going back to him would just be proving Batman right to believe that Robin cannot be a stand alone hero nor mantain a team. And we know how comically big his ego is (Robin's) and how petty he can be too, so he wouldn't just suck it up and accept defeat like that.
We saw what happened when he leaves the team too. In "Multiple Trick Pony", when Kid Flash took over the team, Rob was just wandering around Jump City, when he could have just went with Batman supposedly. So that just proves my point.
And also there's the fact that Batman is neglectful as shit canonically and most likely abusive, so going back there would probably not help. Best case scenario Batman just ignores his existence. But this one doesn't matter that much because it's not something Robin is aware of anyways nor he would go back there, but still important to note that it wouldn't be a good option for him even if he decided to go.
And with his only available options out of the way, he would most likely end up homeless, and most importantly alone. That's the main reason he doesn't just leave, but it's not the only one. We also saw in "The Streak", but most importantly "Flashback" that he struggles a lot to find a team that isn't the Titans. No one can stand his personality, and those who can aren't exactly the best heroes (one of them being Santa Claus, who ending up being a villain btw) without counting the Titans ofc. And we know from the movie that his main goal, his big dream and reason to keep going on in life is being a good and respectable hero, but he knows he can't do it alone as he's (unfortunately) not good enough yet to be a stand alone hero. But because nobody BUT the Titans would want to be with him, leaving them would mean leaving behind his dream, which he's determined to get. That's why he pushes through the mistreatment. That's why he doesn't do anything about it other than yell and sometimes fight back, which doesn't stop it from happening again. And atp, because he has this way of living; screams, violence and stress 24/7, he has this normalized and doesn't even realize he's technically being bullied. You could say that he deserves it sometimes because he starts it, which is true, but specially after season 5, the show starts to make others bully him without an actual understandable reason, and it gets way worse than ever before. In an episode he doesn't even deffend himself, and in another he straight up agrees with their derogatory comments (which is huge because his ego normally would make him refuse to even consider those comments as true), which I think just shows how he has gotten used to this and is probably tired of reciprocating all the time, so he just takes it and brushes it off, or starts thinking that some may be true💔.
The whole bullying thing is just sad. It's a situation where he doesn't see how actually bad it is, and because of that he doesn't see a reason to leave, and even if he had he would still be unable to go because he would have nobody at his side. And he can't even try to talk about it with his team so they can tone it down because he has this so normalized that he doesn't see a reason to do so. To him this sucks but there's not much he can do about it and "it's not that bad anyways".
Also, it's not only Robin who has this normalized. The Titans themselfs also have this behavior normalized, as none of them really had a talk about their behavior ever. Starfire at some point just started copying her teammates without being taught that what she's doing is wrong. Beast Boy and Cyborg don't see it as that bad. And Raven is a weird case because her character after season 5 was completely lost. She acts way different from herself of previous seasons, so idek how can I explain why she engages in the bullying because I genuinely don't know. Best I can come up with is that her lack of empathy for others plays a part in why she started doing this (+her being raised to be a bad person by her father), and her becoming "closer" to the team made her want to engage with them too (obviously i'm reffering to times when Robin didn't deserve the mistreatment, or did but they went way too far with it. Every other time is deserved).
Worse part of this is that if only one of them realized how ACTUALLY bad it is and communicated it, this problem would be easily solved. But well I doubt that'll ever happen.