Yeah, his analogies are always awful and I don't get why this logic escapes him. Well, I mean, I guess I do know why.
If someone comes in his chat and he, as the moderator and final arbiter of his stream, decides that someone's vulgarity, insults, etc. warrant banning them, then how come him responding with the same behavior doesn't warrant banning from Twitch, as the moderator and final arbiter of their site? Which, as has been said, they didn't even do. They just said they weren't going to remain in a partnership and give money to him for that kind of behavior.
This is just more proof that his criticism of other people as not knowing how 'the real, adult world works' is hilarious. He's barely ever had a 'normal' job, so his frame of reference for conduct in a workplace is him sitting on his couch and calling people idiots and he thinks that's how the whole world works. He actually thinks if some customer or client is being abusive and you, as an employee, respond by telling them 'get the fuck out of here you fucking piece of shit', that you have some justifiable moral high ground, when the reality is that whoever you're working for probably doesn't want ANYBODY yelling and swearing and causing drama in the middle of their place.