Just don't SQUEEZE so hard. It ain't blacksmithing...
We are talking about bending a tiny sliver of metal out of the way. In my experience the point of the barb most often curls down leaving a bump. That is all that needs to be done to make the hook in effect, barbless.
That takes MINIMAL pressure. I've done it at home with a TINY pair of smooth jaw long nose pliers I have at the bench and in the field with my smooth jaw hemostats.
If you are trying to make the barb totally flat, you are looking for trouble...
I also concur with Lefty's Kreh's advice to put the pliers in line with the hook point versus coming in from the side. This ensures the most pressure will be on the point of the barb versus where the barb joins the hook.
A couple of other S's that will help:
Smooth Jaws - Smooth jaws are ALWAYS the preferred tool for wire bending of any kind. Serrated jaws MAY scratch or nick the metal creating a weak spot, resulting in breakage.
Small Tools - Smaller pliers or hemostats make it harder to apply pressure. If the steel in the tool handles is slightly flexible, that is better and if the jaws are parallel, that is best.
S-L-O-W-L-Y - Squeeze down the barb slowly & lightly versus fast and hard. Check it, and if the barb isn't out of the way, do it again with even lighter pressure.
Good luck!!