Adept
Master Black Belt
Its a show of respect. I'm going to take a shot in the dark here and assume you are not asian. Ask your instructor why you don't where shoes in the dojang or your school.
99% of asian households don't where shoes in the house; your school should be just as sacred.
That doesn't make a whole lot of sense to me. Sure, it works for asians where wearing shoes indoors is not the norm, but here in the west?
Personally, the only reasons I can see (pragmatically speaking) for not wearing shoes during training is that 1) a tennis shoe hurts more when it hits you in the face and that 2) it makes the floors harder to keep clean.
In an attempt to 'evolve' I think most training should be done in shoes. You are more likely to be wearing shoes when you have to use your skills, and wearing shoes can significantly alter how a technique should be executed.