There is a good chance the rope ran across the nose of the biner, since it was back clipped. This might explain the core shot. The poster is lucky the rope didn't unclip from the draw.
This was my first thought. It may have pushed the gate open and started unclipping itself, but got caught up on the biner's nose. If you were back-clipped, you're lucky you got off with just your rope getting messed up.
It is hard to say exactly what happend here... The rope catching on the nose of a carbiner as it started to unclip sounds likely.
Things to take away from this 1. Dont back clip 2. Inspect your rope after every use 3. 2 years on a rope seems like a lot, not sure how much and how big of falls you are taking, but I can tell you a rope for me goes 1 year max.