Why did he kill his own mother?

Penny is not mentally well as a person as she possibly has schizophrenic and narcissistic tendencies hinted in the film. She is shown to be neglectful as she didn't save Arthur as a child from his abuse, it's unknown why she didn't but it's presumed she was abused by him as well, causing her mental problems.

So she should not have been killed, since she was just sick and not evil.

So stop playing with your mini dick BenStrousers and pay attention.

don't come here with your 52 posts and throw insults around, and especially not at me.
Your pm's are reported as well

it was not nice :-(

and silly as well, because he was really worried for her at the hospital, then only a short time later he killed her in the very same hospital.

it was a stupid move by the director/screenwriter..... even a sick man like arthur would not kill his mother just because "she did not stop the abuse"

he had only her, and he would love her no matter what.
only part of the movie i have a problem with .

She didn't lie at all -- Thomas Wayne was clearly the father and covered it up. Who lets a single mentally ill woman adopt a child? Think about it -- it's an Arnold Schwarzennegger type situation, rich guy plays around with the maid, then tries to avoid the consequences.

Not if she is so ill that she believes it's the truth