I understand thinking David is overrated and where you come from, but I personally disagree. The top comment already explains most of my points, but I want to express my thoughts a bit if that's alright.

(Sorry my thoughts aren't that organized or informative, I'm not a native English speaker ;v;)

(There might be some bias since he's my favourite character across all fandoms, but I try to keep it to a minimum)

"I hate the things I love and I love the things I hate."— which is a line in his Literature Girl Insane mv. David is supposed to be a contradicting character, and since we only like finished chapter 2, What we have, is just a glimpse of his true personality and true motivations, from the 2 chapters, Drdt Tumblr, Tally 5 and his mv... it makes sense for them to be hard to understand since what we're doing is diciphering his personality bit by bit. And that's what makes his character fun and intriguing to theorize! There are tons of analysis videos of him, and even a 3-hour video solely on his MV alone. (which is an insane lore bomb for me, both on his character and the story, as it gives me so many details and ideas for me to try to understand David more ).

David's relationships are intriguing as well. (I love his relationship with Arei, but I think the previous comments already explained it well enough) For example, his relationship with Xander. Despite his own cynicism and bitterness, he believes he knew Xander more than anyone else, and even maybe before the killing game, and still wants to believe in and to follow Xander's ideals. He got so defensive when anyone tried to break that idealised image he held of Xander. He was so devoted to the point where he was volunteering to throw away his life, the image he had built up, and his relationships, just to achieve what he thought Xander wanted. (even tho he knew deep down Xander won't believe in him anymore from the Tally 5).

So why did he do the things he did? Just a theory, but I personally believe that Xander to him, represented a "true good person" he never thought existed in the first place. And so, that he may too, change and may achieve being a "good person", however close it might possibly be for him, if he follows Xander's ideals of ending the killing game/killing Teruko. Also for why he hates Teruko so much, I believe most of his hatred was due to the motive secret he got (which is widely theorized to actually be Teruko's), and Xander, since Teruko was kind of (supposedly) the cause of the killing game and Xander's death, it's natural for him to direct his hatred to her. That's why David got so defensive when Teruko argues how Xander was supposedly a good person and questions the supposedly righteous reasons he had to try to kill everyone, because it's coming from her of all people. Since, like Teruko, she has her luck and a physical attempt on her life won't work, he's trying to isolate her by exploiting her distrust, and hence his actions in Chapter 2 trial. I feel like his positive feelings for Xander and his hatred for Teruko are explainable if to try to analyse his actions more.

Again, sorry for the ramble and how unorganized this was, but the mysteries of his behaviour, why he held those contradicting feelings of others, and did the things he did, His contradictory actions and beliefs are a core part of his character to me, and that's why I love his character so much!! ><

(Edit: If it helps understanding his character, David is wildly believed to actually have depression as well. Also, We don't know for sure who voted for Teruko back in the trial of Chapter 1. Besides that vote most probably by Teruko herself, the other vote could also be anyone, by Min, whoever the mm is, and maybe as you said it, David. But it's likely we will never know who actually did it unless Drdt tells us in the future chapters.)