Secondary Click does not work properly!

When I right click the mouse (tried with several different mouses from different manufacturers - same problem) or press the trackpad with two fingers, it shows the desktop instead of opening context menu. I also checked my mouse on another macbook - no problem there - so obviously mac problem, not mouse problem.

Trying to change that to normal functionality, I opened the mouse section in System Preferences.

However, there is no such option there. The ONLY options are: scroll direction, scroll speed, track speed, double click speed, and primary mouse button.

I tried the trackpad window, but there is no way there to change what certain gestures DO, just to change which gesture activates which action. I tried to untick "secondary click" there - so secondary click on the trackpad stopped working, but the right mouse click still shows the desktop!

I looked everywhere and searched google for hours and asked the former owner - to no avail.

How do I make right click do what right click is supposed to do?