Metal does not equal goth rock music. If it said Gothic music I would not be so cruel. Though I am no genre nazi I know my genres and I understand people freak out but like anything else genres are created to define the technical aspects and lyrics ideas of music. Gothic Rock or Goth Rock is mellow and punk influences music. Try listening to some Faith and the Muse or Christian Death (with Rozz Williams) or maybe some old school like Bauhaus and Sisters of Mercy.

Joy Division is consider old school post punk/ goth rock. They created the scene which we consider goth scene. Though at the time there music was punk but latter on in the 80s the subculture following bands like Siouxsie and the Banshees and Bauhaus were consider "goth". Similar to idea of Hip Hop Culture and Punk Culture and Metal Culture etc... Each has its own style, flavor and following.