Another way of softening the jaws of the hackle pliers that has worked for me over the years is to slip a short section of heat shrink tubing over each side of the jaws. Heat the stuff up and it shrinks to a perfect fit. Shrink tubing can be obtained anywhere electrical supplies are sold. Radio Shack etc etc
If it is the hackle stem that is the cause it is often the hackle is too dry and brittle. Try either soaking the hackle stems in water for a while beofre tying or soaking them in a jar with water and a little hair conditioner. Then lay it flat on a paper towel to dry. When using hair conditioner, pick the one with the least amount of smell, as you don't want a perfumed scent to the fly.
One way of testing what it is that is breaking the hackle is to wrap the hackle by finger only. If it breaks with fingers, it is most likely dry brittle hackles. If the pliers are breaking it and not the fingers I suspect the pliers are to blame and would use the heat shrink tubing to correct the sharp edges of the pliers.
Tight Lines and Screaming Reels!!!