On completing the doctorate in 1979, he was sent to teach in the Regional Seminary of Papua New Guinea and the Solomon Islands for three years as Professor of Dogmatic Theology.
Twomey also said that "the longer they delay in doing so, the greater the damage they will do to all faithful Catholics, and in particular to the survivors of abuse who are still paying the price for the sins of their priests and bishop".
Worse still, there is a marked general tendency in the Irish Bishops’ Conference to hide behind the episcopal bench, as I pointed out in a public debate in Maynooth".
[3] In an interview on RTE Radio 1 following publication of the 'Cloyne Report' in July 2011, he opined that the current Minister for Justice, Alan Shatter, did not understand the "seal of the confessional" as he was not a Catholic.
In a letter to The Irish Times, Twomey wrote: "Since I am on record as calling for the resignation of the bishops mentioned in the Murphy report (3 December 2009), I should have expressly excluded Dr Martin Drennan.
He said moral theology was about virtue, decency, character, principle, but that "very little of that has been evident in the last 20 years, be it in banking, economics, politics or the church".
[6] In March 2012, after being contacted by Atheist Ireland, Hibernia College removed material on atheism, written by Twomey, from its religion module for primary schools teachers.
The material, Atheist Ireland argued, was defamatory and untrue, linking atheist humanism to both Nazism and Communism and accusing it of "producing the worst horrors history has ever witnessed, namely Nazism, fascism and Marxism, the latter alone responsible for some 100 million lives, according to The Black Book written by French ex-Marxists.
In order to pass the accompanying exam, students were required to answer "true" to questions such as "Atheist humanism produced the worst horrors history has ever witnessed".