Nevermind

Why did he do it ?

That's a good question, wait for the story to unfold. Raws doesn't explain much but it's the same insecurity heeseo has & he's got abandonment issues with Taekyung so there's that obsession festering in him slowly

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The real explanation was not given, but if we analyze the situation created we can deduce that:
(my thoughts) Haesoo discovers that his mother didn't commit suicide but that she was killed by Taekyung's adoptive mother. Uke deduced that she was her mother but not having enough evidence he can't blame her. He goes to talk to her and her mother tells him that she has cancer and that she has little time left to live (it will be false because she will be treated and she will also run for governor). Here Taekyung seems to choose not to reveal anything, having become an accomplice himself (as he will not report anything to the police of the new discoveries or facts about the case) and returning home he finds Hee-seo now mentally destroyed who tells him that he will forget everything regarding the murder of his mother (and uke's mother) if he stays with him but Taekyung says to leave his house and live alone. Hee-seo probably saw that uke chose his mother (despite the murder) and abandoned him. Hee-seo initially threatens to commit suicide, but uke smiles and says that he hasn't grown up yet and that he doesn't believe him and starts to leave home.
It is here that Hee-seo stabs him, probably so as not to be abandoned, due to his obsessive love for him but it will certainly be explained better in the second season.