Getting bad feedback hurts. To try and deny it is not sensible. To see a normal human reaction to rejection as unprofessional or a sign of unfitness for a writing career is very unrealistic, imo. Rejection hurts, no amount of mental training will prevent that instinctive response. That's the basis of the human psyche. If we don't hurt, then we become automatons.
But SeeFacts converse argument conceals a point (although not presented in his usual clear style) in that we as writers can use that normal (and permissible) short-term pain to our long-term advantage by spurring us to push out work to new sets of producers' eyes.
Sometimes I have dark days when I can barely function as a person BUT I accept that these times come and go with little ability on my behalf to prevent those 'moments'. However even in the worst periods, I still write and produce work that will become the basis of a new project. I want writing to be my career, so like all jobs I produce whether I feel like it or not.
There I think is the key to determining whether writing is the job for a person. Not the length of time that you experience pain over a rejection but whether, even in your worst moments, you can be found writing then you are a writer, however successful or unsuccessful the world views you.