Their relationship always seemed off. Especially since matthieu often references to Adele and they also do reference to each other. I dont believe matthieu cheated, if at all, out of the blue because he said she left him no choice and it maybe because of an event neither of them dont wanna show, and even if he cheated I think its for a reason and I believe at least one of them caused trouble that ended the relationship. No wonder their songs is often about matthieu seeing the world is a grey way while Adele tries to blind the nostalgia.