Facebook often says you’re online when you’re not, and this can cause problems. explained here how to sign out of messenger on all platforms.
Sign out of Messenger on a mobile device
While it may seem perfectly sensible to expect the sign-out setting to be in the Messenger app on your smartphone or tablet, that’s not the case. Instead, you’ll need to go through the Facebook app.
To find the option to sign out, open the Facebook app and then tap the three-line icon (bottom right on iOS or top right on Android).
Select Setting > Security and login.
You will now find, under the heading Where are you logged in?, a list of devices and locations that are currently active. Under each device name, you should see if you’re signed in to the Facebook or Messenger app.
Find the one you want to remove, and if it doesn’t appear as the two most recent devices, tap the option See everything.
Find the latest Messenger entry and tap the three dots to the right of its name. This opens a dialog from which you can tap Sign off to deactivate the session.
Sign out of Messenger on a laptop or PC
If you don’t have the device you want to log out of, you can still disable it through the Facebook website. To do this, open your browser and go to Facebook. With your account signed in, click the down arrow in the top right corner and select Settings and privacy > Setting.
On the next page, you will see a column of options on the left hand side. Click on Security and login.
Now, from the section marked where you are logged infind your device and click the three dots to the right of its name, then select Sign off.