It's always an oxidizing agent. In H2SO4 sulphur is in +6 oxidation state. To act a a reducing agent one should lose electrons i.e; the atom should go from lower positive oxidation state to higher positive oxidation state. read more
Oxidizing acids, being strong oxidizing agents, can often oxidize certain less reactive metals, in which the active oxidizing agent is not the H+ions. For example, copper is a rather unreactive metal, and has no reaction with concentrated hydrochloric acid. read more
It is an experimental fact that the same substance may under properly chosen conditions act as an acid, a base, an oxidizing agent, or a reducing agent. For example, water acts as an acid toward ammonia, as a base toward hydrogen chloride, as an oxidizing agent toward active metals, and as a reducing agent toward fluorine. read more