There's a difference between general anesthesia and general sedation. Sedation is more commonplace and the anesthesiologist uses a cocktail of drugs to knock you out, but it doesn't totally shut down your CNS (central nervous system). General anesthesia requires intubation because the drugs are powerful enought to stop all reflexive and autonomic behavior, including peristaltis (muscle contractions in the intestines and elsewhere) and breathing. For gynecomastia surgery this is overkill.
Make sure your doc was talking about GA and not sedation first. If he's stuck on GA then you can look for another doc. If it's sedation and you're still anxious about it, it's a bridge you'll have to cross if you want the surgery. That's your call.
BTW, when I went in I wasn't nervous at all until I was finally in the waiting room outside the operating room. The anesthesiologist came in, asked a bunch of questions, started an IV and gave me a shot of something reeel niiiice. No worries after that.