How do I add FormClosing event?-Collection of common programming errors

That is very strange behavior. You can try adding event handler from design like this: Open form in design view, open properties window or press F4, click event toolbar button to view events on Form object, find FormClosing event in Behavior group, and double click it.Also try the same thing on new form and also on new form in empty project.

If you still have this problem then that is surelly problem of your VS installation.