I think it's a combination of things
1. The first being Hayden's death Theo put the idea in Liam's head that if Scott were to bite Hayden she would live but Scott refused to do so, so then Theo put the idea that if Liam could become an alpha he could save Hayden
2.the fact that Liam was a werewolf with ied on a super moon while his girlfriend was dying, werewolves already have anger issues and can get violent when angry, so Liam having ied just makes his anger even worse than the average werewolf would also we've seen how werewolves especially more newer ones act on the full moon liam in season 5 was still having issues with control but it wasnt just a full moon it was a super moon which is even worse then add on to the fact that his girlfriend is dying then yeah liam has a lot going on in his head, then you have theo who sees all this happening in liams head and puts the idea in liam to kill scott giving liam a way to not only save his girlfriend but a place to direct his anger at
It's kinda what masons says the next episode that while Liam is partially at fault their were to many circumstances.
(also sidenote I don't know if this is kinda messed up to say but I kinda get why Liam was so angry at Scott, Scott had a possible way of saving Hayden Scott said he couldn't cause she could die from it but she was already dying , like she was gonna die either way but at least by biting her she has a chance. I'm not saying that to justify Liam's actions obviously not nor am I saying this to hate on Scott I actually really like Scott and I do kinda get why Scott didn't bite her I just think he should have taken the risk)
how did Theo get into Liam's head? How did he manipulate him to almost kill Scott? were those short conversations we see on the show really all it took?