But that might be a douchebag move.

Sorry but he sounds like the douche if he would assert something like this: "He is really clear on that if I leave, he is going to perform the song with other bands, because he now “owns” half of the songs"

Any self respecting musician who respects their fellow band mates would never pull a move like that. Legally speaking, if you two did not have an "official band" with a specific leader/corporate organizer, then you both only own the parts that you specifically worked on, which from the sound of it, you did most of the work other than the lyrics.

He honestly sounds like a dick the way you described him, and not somebody I'd personally want to work with.