Twitter will not let me sign out?

[Intrépïd]

Alternate way to sign out is to clear ALL your cookies and cache.

FOR FIREFOX
At the top of the Firefox window, click on the Firefox button, go over to the History menu (click on the Tools menu in Windows XP) and select Clear Recent History....
Set Time range to clear to Everything.
Click on the arrow next to Details to expand the list of history items.
Select Cookies and make sure that other items you want to keep are not selected.

FOR CHROME
Click the wrench icon tools menu on the browser toolbar.
Select Settings.
Click Show advanced settings.
In the "Privacy" section, click the Content settings button.
Click All cookies and site data to open the Cookies and Other Data dialog.
To delete all cookies, click Remove all at the bottom of the dialog.

FOR IE 9,8,7,6
http://support.microsoft.com/kb/278835