McLuhan didn't talk much about his conversion. Does anyone have any information about his reasons or how this happened?
What led to Marshal McLuhan's late adult conversion to Catholicism?
The short answer is G. K. Chesterton (amongst others).
Conversion is a deeply personal journey, often taking many years to reach an outcome. But it is certain that G. K. Chesterton started the ball rolling.
What is often overlooked is that McLuhan was an ardent convert to the Catholic Faith. Born in Western Canada in 1911, he was raised in a generically Protestant environment. By the time he attended the University of Winnipeg in 1928 he had no interest in religion. Just prior to going on to England to study at Cambridge, however, he chanced upon the works of an author who changed his whole view of reality: G.K. Chesterton.
In the common sense, wit, and striking paradoxical expressions of Chesterton, McLuhan discovered the wonder of the real world as created by God and full of meaning. He was also introduced to the crucial role of the Catholic Church in fostering learning and culture in European history. By the time he left Cambridge and returned to Canada in 1936, he had an intellectual conviction about the Church. But he felt no personal need for religion.
When friends asked him, "Why aren't you Catholic?" he was as puzzled as they were. Then he realized he couldn't have Catholic faith by looking at the Church "from the outside." He needed to approach the Church on her own terms, with the realization that faith comes from grace, and in order to receive this gift he had to pray. So McLuhan began praying, and thereby he entered into the Church's life and felt her maternal embrace. He also met a priest, Father Gerald Phelan (later his colleague at the University of Toronto) who guided his discernment and baptized him when he finally found faith in 1937. - Great Conversion Stories: Marshall McLuhan
Other articles can be found on the web and most imply the same rationale, more or less:
I was reading [G.K.] Chesterton, and [Christopher] Dawson and [Jacques] Maritain and those people. That’s how I came in.
I had no instruction even from clergy at any time but there was a friend of mine who said, ‘Well, since you don’t believe in Christianity’ – I was an agnostic – he said ‘you could pray to God the Father. So you pray to God the Father and simply ask to be shown.’ And so I did.
And I didn’t know what I was going to be shown, all I said was, ‘Show me,’ and I didn’t ask to be relieved of any problems. I had no problems. I had no belief and no problems.
Well I was shown in a quite amazing way and quite unexpected: I was arguing about religion with a whole group of grad students one night at Wisconsin and one of them said to me suddenly, ‘Why aren’t you a Catholic?’ and I shut up because I didn’t know. Up to that moment, it had never occurred to me that I would ever become a Catholic. But I was suddenly caught. I became a Catholic at once within a few days. - Marshall McLuhan’s Catholic Faith