John Tyler was the first to have a veto overridden.
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For the president the advantage would be that pocket vetoes cannot be overridden by congress. The pocket vetoed bill simply disappears until it is started again in another session of congress. A normal veto can be overridden but only about 4% have been.
While President Hoover did veto the Reconstruction Finance Corporation bill, it was passed over his veto. He had already been defeated by Franklin Roosevelt the previous November and was only president for one more month after the veto.
Veto
per the US Constitution, the President can recommend laws to be acted upon by the Congress, and he has the power to veto legislation made by the Congress that he disagrees with
Legislative/Congress