On September 25, 1962, he was named a bishop along with other progressive priests, including Eduardo Pironio and Antonio Quarracino, both later cardinals.

[4] Luro recounts that in 1967 he had a confrontation with the papal nuncio, Umberto Mozzoni, but she gives no details except to say that it was decisive for his replacement as Bishop of Avellaneda.

According to Ezequiel Perteagudo, this was part of an agreement between President Juan Carlos Onganía, Archbishop Antonio José Plaza of La Plata and Archbishop Mozzoni, whereby the government took no action with regard to the 1965 crash of the Banco Popular de la Plata in return for the removal of Podestá;[6] and Luro said in a book published in 2011 that Podestá's removal by the Church was paid for by a government subsidy for the Catholic University of Argentina, and that Plaza gained by the government covering up the bank affair.

[citation needed] Sources cited by the New York Times blamed his removal on his "outspoken attacks on the Government's economic policies", his appearance at labor union rallies, and the influence of conservative Catholics who opposed his enthusiastic support of the Second Vatican Council's reforms.

[5][6] Podestá denied charges that he maintained contact with the followers of Juan Perón, who had ruled Argentina from 1946 to 1955.

Church officials suggested Podestá had resigned due to health problems and denied any pressure from the government.

[12] Podestá was the president of the Federación Latinoamericana de Sacerdotes Casados (Latin American Federation of Married Priests).