In addition to the distinctions listed by Ricky here, I would also add that occupation is slowly drifting away as common usage, at least here in the United States. Although 'occupation' is still a perfectly valid thing to say, the prevailing idiom leans toward what your teacher said. This is just a nuance, but I think it's relevant.
Additionally, I think there might be a bit of a sour taste in how some (many?) people currently associate the word 'occupation', due to various world events of the last several years (regardless of where those people might stand on any political issues). Again, this is a nuance, but language use is built upon such inscrutable things -- and avoiding negative associations when discussing your job is never a bad goal.
All the best, and good luck with your further studies. :o)