He's a time traveller. Any time traveller could meet him/herself & several have done so. It's generally a bad idea, because it's dangerous (especially for those who don't know what they're doing), but it's perfectly possible. Among those who've done this (apart from the Doctor) are:
- The Brigadier in "Mawdryn Undead" (giving a demonstration of one of the dangers);
- Rose Tyler in "Father's Day" (giving a demonstration of another of the dangers);
- River Song in several stories, including "The Impossible Astronaut";
- Amy Pond in several stories, including "The Big Bang";
- Jo Grant in "Day of the Daleks" (causing her some confusion but no other ill-effects) &
- Ace in "Relative Dementias" (novel) (demonstrating that she did more or less know what she was doing).
This is by no means a complete list.