The Thing was great. But not top 3. Sorry. Nope.
False!
I've argued that The Thing should not be considered a "horror" movie in the past, falling under the sub-genre of Sci-Horror rather (like 'Alien', 'Aliens', 'Event Horizon', etc.), but I've since come to my senses. Not only is it (and 'Alien' for that matter) a horror film, it is one of the best ever. In fact, I'd rank it top 2 along with Carpenter's other seminal classic 'Halloween'. To say that it isn't a top 3 horror film is insane. You mentioned 'Phantasm', and although I love that film and it is one of my top 10 horror films of all-time, it does not hold a candle to John Carpenter's 'The Thing'. 'The Thing' was not only claustrophobic, but it evoked a sense of paranoia in the viewer that no other film before or since has been capable of doing. Not once during the film did you know who was or was not
The Thing and each reveal was a shock and the film was masterfully directed by Carpenter and equally masterfully scored by Ennio Morricone. Not to mention it had some of the most gruesome and amazing special effects by Rob Bottin, a protege' of the great FX master Rick Baker.
Here is my horror top 10 (not including Universal Monsters films) -
1. John Carpenter's Halloween
2. John Carpenter's The Thing
3. Alien
4. A Nightmare on Elm Street (1984)
5. Night of the Living Dead
6. The Texas Chainsaw Massacre
7. The Exorcist
8. Phantasm
9. The Conjuring
10. Sinister