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 device or session
Tap Log out
On Android, you can also go to Settings
Tap Apps
Tap Messenger
Tap Storage
Tap Clear data or Clear storage
On iPhone, you can uninstall the app to sign out locally
On desktop, click your profile picture
Click Log out