Make an excel spreadsheet. Just pick a school and calculate the costs. do the math for repayment (don't forget to subtract the cost of health insurance and stuff!), throw in a 2 year residency, and show them that you'll be like 38 by the time you pay everything back.
Compare that to a nice spreadsheet of how life would be if you paid off your service-debt by age 29 via Navy. Show them how much money you'd have in your bank account.
Parents like spreadsheets - I showed mine to my conservative Asian parents and they gave me the thumbs up.
Or just say that your current university needs a copy of your birth certificate to apply for graduation this may or something like that.