I wonder if he meant a psychologist or counselling which could help anyone to work out for themselves what they are and what they want. That's the point of it, talking to someone neutral helps. A psychiatrist is a medical doctor, quite different. I didn't get that Pope Francis was suggesting anyone could be somehow 'medically' changed or even talked out of being homosexual (or advocating conversion therapy). It's not a mental illness.
(He could have been out of his depth too.)
What he said probably lost something in translation and the headline 'Don't condemn your children for being gay, whisk them off to the psychiatrist' is sensationalist.