The person standing in front of him looks exactly like the Doctor, right down to the last hair on his head, except that he only has one heart while the Doctor had two. His almost identical twin, created when he siphoned excess regeneration energy into his handy spare hand.
Only the universe isn’t big enough for two Doctors, especially when one is half human, so what can the Doctor do with him? It’s a bit of a dilemma.
The only logical course of action is to send his other self somewhere else, the alternate universe, his parting gift to Rose.