I am going to kick my friend out of our friend group.
What is your reason for wanting to exclude your friend from the group?
He is a very negative person and he relies on others too much. I don't want to listen to his self-pity anymore
Its not very nice to exclude your friend from a group. However you can choose not to associate with them if you feel like he is affecting you negatively. Make the decision that would make you happier.
You are telling me that I can't be alone. I thought I was just being a selfish douchebag but you are making it sound like a social moral thing.
Your friend trusts you, and turning your back on them in this way could really make them upset. If they are upsetting you then you are better off having a conversation with them rather than simply cutting them off.