How to Log Out of Facebook Messenger – Lifewire

For whatever reason, Facebook has designed its Messenger app so that you can’t log out of it — at least not with a direct logout option available within the app. There are, however, a few tricks you can use to disconnect your account from the Messenger app (which is essentially the equivalent of logging out) without having to delete the app from your device.

https://www.lifewire.com/how-to-logout-of-facebook-messenger-4153087