DISCLAIMER: Slur! Speculations! Rumours! Jokes! Yada... yada... yada... BE WARNED!
It looks like Yance has some unresolved issues with his grandmother, who was apparently practicing her pickpocket skills on him, probably stealing his lunch money, so he would have nothing to pay a school bully. It is quite clear how he ended up being together in the same organisation with a bunch of mental cases like Vico and Jacia.
Yance doesn't really teach the princess how to pickpocket during his lesson. Anyhow, she usually does pick something up during this lesson, but that is what warm baths and remove disease potions were invented for.