The middle mouse button has been around forever.
All X11 workstations had one. Because of this, X11 is built expecting a middle mouse button as the paste in terminals. That's standard X11, not Linux. Because of crappy two-button-only-mice, XFree86 and XOrg has a setting so that pressing both Left and Right at the same time emulates a middle mouse button click, but it needs to be enabled in the config files.
You could almost always find a PC mouse with a middle button and you damn well needed one for high end applications. They weren't quite so common because (a)many mouse makers were cheap and (b) there was the "average computer users are morons" philosophy. In other words, two buttons would be less confusing than three.
Then the scrolling wheel was introduced and, what the heck, lets just make that a mouse button too.