Open the Messenger app
Tap your profile picture in the top left
Scroll down and tap Account settings
Tap Password and security
Tap Where you’re logged in
Select the Messenger session or device
Tap Log out
If needed, use the Facebook app or website to log out of all sessions
On iPhone, you may also remove the app from your device after logging out
On Android, you may also clear the app data if you want to fully reset the login state