Originally Posted by
Sheldon Brown
Simple cantilevers, either cable style, move in a circular arc centered on the frame/fork boss......
If you lower the brake shoe to safely clear the tire, it risks "diving" under the rim as the brake shoes wear.
The "Parallel Push" linkage causes the brake shoes to be traveling in a roughly horizontal direction in their normal range of motion. (Actually, it's still a circular arc, but it's centered on the lower, inboard pivot of the parallelogram.)
Sheldon "Geometry" Brown
I believe that is pretty much what I said I had read was the chief advantage of the parallel-push configuration.