Acid when reacts with metal release hydrogen gas but there is one acid which when reacts with metal does not release hydrogen except for two metals. Prove this statement.

Nitric acid doesn't liberate $H_2$ gas, instead you get nitrogen oxides and water along with metal nitrate. This is because $HN{O}_3$ is a powerful oxidizing agent, It oxidises the hydrogen produced to water and itself gets reduced to oxides of nitrogen such as $NO,N{O}_2,N_{2}O$

However dilute nitric acid reacts with Magnesium and manganese to liberate $H_2$

$Mg+HN{O}_3\to Mg(N{O}_3{)}_2+H_2$

From the reaction we can see that, loss of electron takes place which implies that $HN{O}_3$ oxidises Mg. Mg is reducing agent , hence hydrogen is reduced due to reducing nature of Mg .