Mexico is a giant country, and painting it with one brushstroke is idiotic. Most of the very dangerous states are in north, near the US border. However, the vast majority of the country is safe for travelers and many Mexican cities have a much lower murder rate than their American counterparts. In short, avoiding Mexico because of dangerous areas would be like avoiding the entire US because of the crime in Detroit and St. Louis.
Moreover, I can say that I never once felt threatened or in danger in Oaxaca, and I went all over the place, often alone and never felt unsafe- and seeing that I was raised in Oakland and have worked in Compton and the San Fernando Valley, I feel I have a pretty strong instinct for the signs that differentiate dangerous neighborhood from one that is simply poor. The worst crime I heard of occurring to anyone was pick-pocketing, but that happens in all tourist destinations, including a few blocks from my house on Hollywood Blvd.