Only Santiago can fulfill his Personal Legend and can achieve his own destiny in life. The Alchemist can certainly help him along the path, with wisdom, guidance, and moral support. But in the final analysis, it's Santiago who must take that final, crucial step. That's why the Alchemist leaves Santiago alone to complete his epic journey.
A Personal Legend means just that; something that is unique to each and every one of us. It is only right and proper, then, that each individual finally reaches their goal alone. And the Alchemist understands this better than anyone.
His role was to lead Santiago to his destination, but once it was clear that Santiago finally understood where he was going he had no further need of the Alchemist's assistance. The Alchemist's job is done, and so he fades from the picture as Santiago, at long last, fulfills his Personal Legend.