Perhaps you couldn't. I don't see any regulations or requirements that restrict any of these professions to my daughter. I know at least 2 deaf & HOH officers in the USNavy. I know I've read of at least one deaf police officer on this forum. There's a deaf airline pilots association, so assuming that means there are deaf pilots...
Deaf airline pilots ? Doubtful ..
Deaf pilots .. yes .. but not airline.
FAA Medical Certification / Medical Standards and FAA Forms
Requirements for medical certificate.
Demonstrate hearing of an average conversational voice in a quiet room, using both ears at 6 feet, with the back turned to the examiner OR pass one of the audiometric tests below or:
Audiometric speech discrimination test: (Score at least 70% discrimination in one ear) or:
Pure tone audiometric test: Unaided, with thresholds no worse than:
500Hz 1,000Hz 2,000Hz 3,000Hz
Better Ear 35Db 30Db 30Db 40Db
Worst Ear 35Db 50Db 50Db 60Db
As long as all other parts of the medical can be passed normally .. a pilot can obtain a waiver that will mark his/her certificate as
"Not Valid for Flights Requiring the Use of Radio" (14 CFR section 61.13).
Currently all flights in controlled airspace require use of a radio. As I mentioned in previous comments , this may change in the near future as the next generation of ATC systems is brought online.
If you have more information about this 'deaf airline pilots' group , I would like to contact them. A quick google search did not reveal them to me.