Reason to log out: shared computer. That's also when using a computer at school. As said before: you risk account hijacking if you don't logout in that situation.
You remain on the logged in screen, as long as you've a running browser session to the forum. And you may also be displayed active for a few minutes after that as the list has to be refreshed.
When you don't log out, there's still a cookie that does the logging in for you as soon as you visit again. Clearing the internet cache has the same effect as logging out.
The cookie is the remember me function.
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