Why does Copper react with H₂So₄ and not HCL ?

Generally the reaction of a metal with an acid is written as 

 Metal + acid ------> Metal salt + hydrogen gas

Now this reaction is not true for all the metals. Only those metals which are more reactive than hydrogen will liberate hydrogen gas from the acid and form the corresponding metal salt. These metals are placed above hydrogen in the reactivity series. As copper is less reactive than hydrogen, therefore it will not liberate hydrogen gas from the acids like HCl, HNO₃ etc. 

But sulphuric acid is a strong oxidising agent, therefore it will oxidise copper metal to Cu²⁺ ion. However, no hydrogen gas will be formed, only copper metal will be oxidised here. On the other hand, HCl is not that strong oxidising agent, in fact its use as an oxidising agent is not too well known. Hence it does not react with copper metal at all.