Sorry to hear that your experience is negative. Please help to track this down:
Make sure that Firefox is not tricking you here. Having a tab with about:preferences#privacy open while clicking the "clear" button caches the displayed cookies in some way. Opening the 'remove cookies' dialog on this page (about:preferences#privacy) will show cookies - although they're already gone.

Please try this:
- make sure about:preferences#privacy is not open
- open a fresh tab, go to some website and log in,
- browse around to confirm you are logged in,
- open about:preferences#privacy and confirm a cookie from that site has been set.
- close about:preferences#privacy
- then click the "clear"button and browse on that site more - you should be logged out again.
- open about:preferences#privacy and confirm cookies are empty