What makes you so angry about people analysing his character? There is certainly signs of instability in Byakuya himself, I mean who just fucks with a crime scene for fun? I'd like to know why you hate people reading into his backstory, because after what he went through you're bound to be at least *somewhat* hurt on the inside. And what's so wrong with Naegami shippers? Coming from someone who has read into Togami and has analysed him quite a lot, I can see how some view him as a suicidal character.
If you really looked into his character, you would know why he messed with Chihiro's body. Or the fact that he literally says part of the reason in the game... He did that because he wanted to see who could solve the truth, that's what he says in the game.
As for the other part? It was a way to out Genocider Syo/Jill. Yk, the serial killer who murders boys she likes... like Byakuya... It was a way to ensure his safety.
And there's a difference between a bit hurt and actually being very insecure and feeling like he isn't worthy of his title. The first one is fine, that makes sense. But the second... yeah, no. Not with Byakuya. He is confident, practically overly confident. That's his fault, his weakness. Not being an''uwu soft boy' on the inside or some crap like that.
As for the Naegami part, most of the time these mischaracterisations come from Naegami shippers so Makoto can 'make him feel better' or something stupid like that. The idea of Naegami is fine, but the way people make it simply doesn't work and is border-on fetishization. The dynamic people make them have doesn't work. It's just so they can have dominant x submissive or something else like that, though Naegami shippers aren't ready to admit that.
There's a good way to write their dynamic, yes. And I've seen a few people do that, but most don't. Most go for the mischaracterisation to add 'depth' to Byakuya that makes him a different character.
And... he really isn't suicidal. Or we really forgetting his moment in the Chapter 4 trial?
He doesn't understand feelings, he doesn't understand suicide. And what reason would he even have to feel like that? Like, feeling suicidal is a very serious thing and Byakuya simply doesn't fit that bill.
He doesn't mind the situation in the killing game, believing he's above it all and can win. As for his life before? It was perfect- he was perfect. Does that sound like a suicidal person to you? No.
So, that's why I'm angry. Because some people are trying to make Byakuya into something he's not. Maybe in some big AU I can see him being suicidal, sure. But here? God, no. It's not even mischaracterization at that point but a fully different character.
Byakuya has a big ego. He isn't actually insecure. He quite literally believes himself to be better than practically everybody else. Anybody who has even read a bit into his character knows this. Stop trying to make him a fully different character, it simply doesn't work.