The Facebook Messenger app doesn’t have a log out button like the original Facebook app though, which irritates a number of users. In any case, just follow the steps below and you’ll be on your way out.
How To Log Out of Facebook Messenger On Android
Step 1: Head on to the Settings menu of your mobile.
Step 2: In Settings, scroll down to the Apps or Application Manager, and scroll down until you see Messenger.
Step 3: Tap to the Storage menu as shown in the image above.
Step 4: You should now observe two options – “Clear Data” and “Clear Cache“. Just click on “CLEAR DATA“. Now when you go back to tap on Messenger in your app drawer, you should see that it won’t log you in automatically.
And, you have successfully logged out from the Facebook messenger app.
Read more about facebook messenger.