You would need to be either really careless or a total clutz.

Don't get heavy handed. Let the reamer work itself in under very light pressure. If it starts to bind stop and take it out turning slowly to the right. Don't ever turn it backwards. Clean it and chamber with spray solvent, then give cutter a coat of cutting oil and start over. Don't put any side pressure on it. The pilot and cutting flutes will stay aligned easily. Use a good tap handle. Not vise grips or pliers or a crescent wrench. A padded vise to hold the cylinder is needed to hold the cylinder steady at the same angle. All this helps keep it all aligned. When the little step in the reamer that cuts the recess touches the bottom of recesses. Stop , your done.

Thing about re reaming the chambers is you only removing a tiny bit of material. Cutter shouldn't turn hard unless you jam it in hard or put side pressure on it.