The most obvious answer is that it’s made up from carbon that is an element that is non-metallic. Carbon is an element that is not metallic and is very conductor in various forms. In the case of graphite, the molecular shape improves its conductivity through creating the conditions where electrons can be “free” for movement around within in the structure of bulk.
It is not uncommon to find non-metallic elements that create molecules with good conductivity. The term “metallicity” is not determined solely by conductivity but also by other physical characteristics that the elements possess.