Went through the same thing myself recently. You need a special tool to compress the piston. The piston must be rotated as it is compressed (notice the notches in the face of the piston).
The tool is basically a C clamp with tabs that fit in the notches. As you tighten the clamp, you also rotate the piston.
I had to put my old shoes back on until I got the tool. I used a clamp, and rotated the piston with a pair of channel locks. You could 'technically" use that method to compress the piston all the way, but I was afraid I would chew up the piston and cause a leak.
HTH