I'm taking an introductory graphics course, and while I intuitively understand that converting a click or touch into object coordinates will make the math much cleaner, reduce the chances for human error, and potentially make debugging easier, none of these are actually a very good explanation, conceptually, of why object coordinate spaces are used in selection tests, as opposed to simply using world coordinates for the test - rather, they're just observations of what tends to happen when object coordinates are used. So I ask: why?
A selection test involves comparing the click coordinates, which you get in window coordinates, against lots and lots of object features, which are represented in object coordinates.
You need to transform them into the same coordinate system in order to do the checks, so you can EITHER transform the one simple click point OR you can transform all the various object features.
Transforming one point or line is just a lot easier that transforming a whole bunch of object features of various types.