It seems pretty clear to me that his mistake was refusing to essentially tow the line, as a manager I don’t think you have a choice if you give a player an ultimatum of sorts and he doesn’t comply.
If you want to be critical of Arteta it’s probably in creating a situation where it got to that point. He needs to be much smarter about managing difficult players. I personally don’t think it matters with Douzi as I don’t really like him as a player but it could cost us eventually, Saliba is potentially an example. Guys like Douzi and Saliba should be going to war for him, not against him.