It can break down tissue. Incorrect measurements are also a possibility.
And another possibility: binding can cause your ribcage to compress. I don't know if it's permanent or not. I noticed this happening (my ribcage measurement, under the moobs not over them, was 34" before putting on the binder, 32" while it was on, and 32.5" after taking it off. I stopped using that binder because of this (also because it made it too hard to breath). It took about a day for my ribcage to go back to its original 34" measurement; I was worried about damaging something.
Maybe want to go easy on the Ace bandages, they don't allow your ribs to expand like a binder would. Granted, when I was having trouble it was with an Underworks binder, but that one was too small. My other larger one was OK.