The real reason why Arthur became Joker
This is just my interpretation and I’m not sure how many people think like this.
!SPOILER ALERT!
Arthur got shocked after committing murder but soon, he felt relaxed and danced.
Many people think he found real himself through this accident and became Joker, but actually, it is not the case.
He knew what the kind of beings with no guilt about killing people be like and he didn’t want to be like that.
In fact, he agonized a lot. In the mental hospital, Arthur asked the clerk if all people winded up in there were criminals and confessed he had thought he would feel bad about killing people but he didn’t.
Then the hospital document said his mother let him be abused and he got severe trauma to his head.
It was likely that something went wrong with his head at that time.
After realizing his mother, the one he depended on the most and the one who forced him to laugh and happiness, played a big role in making him like that, Arthur completely despaired and gave up his will to be better.
Before killing his mother, he confessed that nothing was wrong with him and that it was what he was therefore he couldn't even fix himself, so all of his struggle to be normal was nothing but a comedy.
It isn’t that Arthur found his real self. He just gave up.