Here is my take on this, for what it's worth:
Perhaps President and Mrs. Bush think that perhaps Shakespeare and symphonies for small towns and rural areas would offer a contrast to the MTV culture and would elevate the aspirations of kids in those areas. Perhaps they feel that this nation's commercial entertainment industry is destroying the public's appreciation of the great inheritance we all share in the arts of Western Civilization.
And just maybe they are doing this because it seems to them to be the right thing to do.
They can make up this money by cutting some other program, and probably will. Since the budget is essentially flat in all non-defense and security areas, I imagine that is what is was done.