What are the pros and cons of high-wing compared to low-wing design?
This is actually a really hard question to answer, as there are a ton of factors. I'll try to cover a few.


Visibility is probably the reason you most hear when it comes to GA pilots. 

High-wing aircraft offer better visibility below the aircraft, especially for passengers in 4-seat or larger aircraft, as the wing doesn't block it. 
Low-wing aircraft can offer better visibility above the aircraft, as the wing remains mostly out of the field of view.
Note that a lot of midair collisions involve mixed types; low-wing aircraft descend into high-wing, or high-wing aircraft climb into low-wing.

Landing characteristics are different, as low-wing aircraft can incur more ground effect than high-wing.
Aerodynamic stability of the two designs differs a bit; the center of lift can be higher in a high-wing design, often offset with dihedral in low-wing aircraft.
Ground clearance (and debris protection), specifically in multi-engine aircraft, is going to be greater when engines are mounted on a high wing rather than a low wing. This is true of both propeller and jet engines, although propellers tend to have a larger radius for a given aircraft size.


There are a bunch more, but that ought to get the argument discussion going.