I think I'm a bad friend
Why do you think you're a bad friend?
I don't include my friend in any events. I think this makes him sad.
It's good you recognize it, but it's harmful to be a bad friend like that. You should try to include him more in the future.
I feel like he would reject if I try to include him.
I don't think he would if it makes him sad. You should ask him just in case.