i don't know if you can make them
understand, but maybe the ADA will convince them tha if you're sensible about what you eat, you'll not die, will remain perfectly healthy, and may be protected against certain illnesses. this page shows the abstract (kinda like an intro) but you can veiw the whole article (not print it though) by clicking on the pdf link. thats enough info for anyone, i'd reckon.
http://www.eatright.org/cps/rde/xchg...3_ENU_HTML.htm
you should also show you're serious about your health and welbeing by getting a book on vegetarian nutirition, and reading it, and applying what you learn. this is a good book to start with- its written by respected dieticians and goes through everything:
http://www.amazon.com/Becoming-Veget.../dp/1570670137
you could also point out that a large percentage of the hindu, buddhist and jain religious groups have been strict vegetarians for practically forever, and they're not exactly dying from it in their millions.
you could also volunteer to key all your daily food stuff into a website like fitday, and keep track your protein and other nutrients- and offer to let them check it to keep tabs on you meeting your requirements. just make sure you are eating properly, or this'll backfire on you (i think you should get the book and work from it first till you're confident with the fitday thing).
incidently, i'm 28, and have been vegetarian since i was 4 (i now eat a vegan diet). my brother is 26, and has eaten tiny amounts of meat about twice in is whole life (less than a mouthful in total- out of curiousity). neither of us has ever had a protein deficiency- and i don't know anyone else who has- it'd actually be really hard to do if you ate enough calories. this site has a nice article about it, and some food suggestions (its got an incredibly easy sample menu at the bottom that shows how easily you could get your protein, too).
http://www.vegsoc.org/info/protein.html