Copper does not reacts with dilute sulphuric acid, liberating hydrogen because copper is lower in the electromotive series than hydrogen.
A more reactive element can displace a less reactive element from its salt solution. The metals above hydrogen in the activity series react with dilute sulphuric acid and dilute hydrochloric acid to liberate hydrogen. The metals below hydrogen in the activity series cannot do that. Copper fall below hydrogen in series.
We can also say that magnitude of the change in Gibbs free energy when a single atom of elemental hydrogen ionizes is greater than the magnitude of the change in Gibbs free energy when a single atom of elemental copper ionizes. Therefore, elemental copper does not have sufficient chemical potential to liberate elemental hydrogen from compounds in which hydrogen has an oxidation state of +1.