actually Fedz sorry to break it to you but metallica and system of a down ARE metal bands.
metallica produced some of the highest rated metal of the 80's,
you might be confused with heavy metal or death metal or any other variation but they are both metal bands.
metallica's first album Kill 'em All was all metal. so was ...and justice for all, Master of Puppets, and Ride the Lightening
while system of a down may have an odd approach to the metal classification they are still metal toxicity, system of a down and steal this album! have some of the best examples of them playing metal.
considering these bands otherwise is like considering iron maiden as rock