While there is no direct log out option in the Messenger app for Android or iOS, this article will show you how to disconnect your account from Messenger (essentially the same as logging out) without having to delete the app from your device.
How to Log Out of Messenger – Log Out of Facebook Messenger
Android users have an easy way out. In the device’s Settings app, there’s a button that will delete your saved login credentials and immediately log you out of Messenger. Here’s how it works:
Open the Settings app.
Tap Messenger. If you don't see it, select See all # apps and scroll through the list.
