It's just not worth putting your parents through that worry. There are plenty of wonderful places to tour in the world, including right here in the U.S.
The big problem in Mexico isn't so much the violence. You probably stand a pretty good chance that nothing will happen. The problem is that if bad things do happen, there is no place to run. Bad stuff can pretty much happen all over the world. But in most countries, at least you have the police (in Italy you have the Carabinieri, those guys are awesome) .
In Mexico the police are most likely your worst enemy or they can be your best friend. The problem is there is no way to know for sure. Pretty much the only people that you can really trust are yourself and perhaps your friend.
Nope I would figure somewhere else to tour to keep your parents happy. But you know they will worry no matter where you pick. That is their job.
Oh and you should be really grateful they are so concerned.