I think, he set himself on fire because he didn't want to become a monster. He is destined to be one and I really do think that he will become monster because bit by bit he is becoming a... half god? I confirmed it when he tried to burn his body but he survived
so helpful. thank you so much! reading this just makes the story have a more intense plot and a deeper meaning. im going to go back and read it knowing what you said and see if i can make more sense of it. them committing suicide was what broke my heart and caused me to break down crying. just so so so sad.
From what i gathered from the manga, the twins, takumi and ayato share the same father as yuzuru.
The story begins with yuzuru as a blank canvas. He has no recollection of what happened in the past until takumi comes up to him, confesses and they end up a couple. (Obviously in this part it was all fast-phased until he locks him up). Takumi begins hinting at ayato who yuzuru has no memory of anymore and only when takumi brought up the part of them going to the shrine and him leaving ayato for dead was what triggered the memory back.
He has recollections bits by bits, which i believe they made quite unclear esp with his mom. (If i'm right she was the one who held the photo and kept saying not forget them- in chapter one the lady who appeared to be his mom doesn't seem to be his mom. They mention that his dad lived in Soudou before getting re-married so i concluded that he got adopted at some point or something) basically, their dad lived in the shrine and was a monster who fed on any living thing. (Some with reason maybe; but others purely to survive because he /does/ get hungry and lose control)
When they were kids it appeared that their dad really wished to see yuzuru. Though yuzuru didn't actually know his real relations to the twins, it was obvious that the twins did. Ayato wanted to be with him and love yuzuru but takumi wanted to prevent them being around him.
Also note that yuzuru blaming himself can be legit with reference to the incidents in his childhood. With the dog that died- it barked on yuzuru when they were passing by the shrine and moriyama whom yuzuru 'didnt really like' (ayato mentioned this); his dad might have devoured them for this reason.
Ayato mentioned about betraying their father (this wasn't explored but maybe something that had to do with keeping distance from yuzuru or bringing yuzuru to the shrine who knows). So, Ayato does bring him to the shrine hoping that seeing Yuzuru would make their father's condition better. But it didn't and they saw him at a bad time when he was 'hungry'. Ayato seemed to be familiar with the trait, which led him to tell yuzuru to run and thus ending up as their father's feed. Their dad, as per the narration, seemed to have lost sense and wanted only to feed that when he realized he ate his own son, cried in the corner of the shrine as he held ayato's bones. Yuzuru didn't seem to have ran off then and watched the whole thing happen and witnessed their father setting himself on fire over the grief of his actions. It was obviously traumatic for Yuzuru thus losing his memory after the events.
As per the fire that happened when Yuzuru went to the shrine again, it appeared that he too attempted to set himself on fire. The doctor said it himself that Yuzuru surviving it is a miracle, with his lunga burned so much it looked like damp firewood and 1/3 of his internal organs chunked out lest he has also "inherited" his father's inhuman/monstrousity conditions. If we consider this then at some point their dad was just a regular guy who fell in love thus having yuzuru and the twins- and only developed to become worse as he aged with time.
Yuzuru then concludes that it was only a matter of time that he too would end up like his father. He doesn't want to be, and he thought that lighting himself up like his dad did could finish the chain of events and also atone for ayato's death even if takumi doesn't forgive him. But it's revealed at this part that takumi is done with revenge because he too fell in love with yuzuru already.
After sneaking out of the hospital yuzuru says his final goodbyes and commits suicide with takumi. It's unclear how their graves ended up in the shrine but as per the flash if events it was obvious that the two boys didn't rest until they found them- leads to the conclusion that they were respobsible for the graves.
In the end, with yuzuru and takumi promising to be together and ending the chain of the happenings, they become the spiritual guardians of the shrine where his father committed suicide. At this point i think they're mostly stopping children from being spirited away since there's no monsters there anymore (plus it's going to be torn down soon).