His early education was constrained by the Great Depression and the family's limited finances, as well as his parents' alleged lack of interest in his abilities.
[citation needed] He went to both state and Catholic schools, including Hawksburn state school (where he won a prize for his essay about The Ugly Duckling by Hans Christian Andersen) and later, when the fees for Christian Brothers College were too much his family, he attended St Joseph's Technical College in the Melbourne suburb of Abbotsford, which he left aged 15 for a job at the Hill of Content bookshop in Bourke Street, in Melbourne's central business district.
[citation needed] During the final years of the Second World War, Conway progressed to electrical fitting in the Royal Australian Air Force which he had joined in late 1944.
He also maintained a busy private practice at his homes in the Melbourne suburbs of Canterbury and (later) Hawthorn, specialising in male difficulties and personal issues.
This association ended when an impassioned censure by Conway of the NCC, particularly concerning the issues of contraception, homosexuality and the parameters of papal infallibility ("Mr Santamaria - And Goodbye To All That", Quadrant, December 1990), led to a lasting estrangement between the two men.
[4] In his books and essays (as the above-mentioned reference to the Quadrant piece implies) Conway questioned Catholic teaching on sexual matters, allying himself with Freud, with Jung (both Freud and Jung are openly praised in The Great Australian Stupor as great pioneers in the study of the human psyche) and, periodically, with Eastern mysticism.
Conway questioned the validity of Catholic teaching on artificial contraception, pointing to the misery of Africa and South America and maintaining that women had the right to regulate the size of their families in an acceptable fashion.
Conway died at St Vincent's Hospital after suffering from Parkinson's disease and peripheral brain damage.