This phrase is generally used to show contempt for someone. Usually, people use this during an argument when they find the other person so pathetic that they can’t believe it.
You are so fucking stupid, that I pity you. You will never amount to anything!
The definition of the word pity implies compassion and sympathy for what someone else is feeling. I think that when most people say they pity someone, they do feel sorry for someone, but to pity someone has a negative connotation to it. When something bad happens to someone you like, you sympathize with them. Nobody wants to be pitied.
Check out these other phrases:
I pity the fool