You can easily chip a knife on a granite counter top. You can also scratch granite with a knife. You will definitely dull the knife edge and possibly ruin the knife eventually. It's also dangerous because the knife may slip as you're cutting.

In terms of dollar per surface area, my knives are worth a lot more than any granite.

When I see people cutting on a glass "cutting board" it's almost as bad as hearing someone run their nails on a chalkboard. I'm sure cutting on a granite counter would get me the same way.