Why does the Lord of the Flies say that Simon will "only meet him down there"?
One of the things that becomes clear through Simon's vision is that the Lord of the Flies, the "beast," is only a representation of the fear and potential for violence that exists within the boys. Simon, as the boy with the clearest vision of things, is the first to make the connection and to understand why things are turning out the way they are. The Lord of the Flies tells him that he cannot really kill the beast because of the fact that it exists in each of them.
And so it is that the beast will not really be there in his secret hiding place where the pig's head was placed on a stake, nor will he find him where the pilot is hung up in his parachute cords. Simon can only meet the beast down on the beach with the other boys because the beast, in fact, exists inside the boys.