It's total pomp and circumstance. Sure, medical school is hard to get into, but that doesn't automatically make the whitecoat ceremony worthwhile. Dental, pharm, AA, PA, and DPT students all have them as well, so participating in the ceremony is no longer a celebration medicine's prestige. The ceremony itself is just an antiquated and melodramatic photo-op. It can be meaningful to your family as others have said, but that seems to be about all its worth.
Look, the nurses are doing it now too:
http://www.remingtoncollege.edu/remington-college-of-nursing-white-coat-ceremony/
I wonder if they'll start having whitecoat ceremonies for the clinical research assistants? Social workers? Speech therapists? The lab techs at the hospital that wear short white coats?