How to log out of the Messenger app from the Facebook website
You can log out of the iOS or Android Messenger apps from the Facebook website, from your PC or your mobile phone’s browser.
Go to Facebook.com, then select Settings from the dropdown menu on the top right. Go to Security and Login, then find the section called Where You’re Logged In.
Find the Messenger session you’d like to log out of, click the three dots on the right, then click Log Out.
There you should see Account settings and Security. Scroll down to Security and select Security and login.
You’ll see a section called Where you’re logged in, then just select the Messenger session and tap Log Out.
How To Clear Messenger app data in Settings
To log out of Facebook Messenger, you need to go into the Settings of your Android device.
Close the app if you have it open, and get rid of it from your recent apps list, otherwise, this trick won’t work.
In Settings, scroll down to the Apps or Application Manager, and scroll down until you see Messenger.
Tap on this, scroll down and find Storage.
After opening Storage select Clear data. There also should be a Clear Cache option, which we suggest you use too.