The origins of both primacy titles dates to the rivalry between both archbishoprics as to seniority. While the Archbishop of Armagh's dominance is due to the fact that his See was founded by St. Patrick, the city of Armagh thus being the ecclesiastical capital of Ireland, Dublin is the political, cultural, social, economic and secular capital of Ireland and has been for many centuries, thus making the Archbishop of Dublin someone of considerable potential political influence with a high national profile.
Within Roman Catholicism, the rivalry was augmented since the 1870s by the awarding to one or other archbishops of a seat in the College of Cardinals by popes. (Due to Ireland's small size, two Irish reigning diocesan cardinals are unlikely to be created.)1 The apparent dominance of Dublin over Armagh was shown in the 1850s when the then Archbishop of Armagh, Paul Cullen was transferred from Armagh to the nominally inferior See of Dublin, he in Dublin becoming the most high profile Roman Catholic bishop. To the fury of Armagh, Cullen as Archbishop of Dublin played a central role in the proclamation of Papal Infallibility in the First Vatican Council and was some years later made Ireland's first cardinal ahead of the nominally superior Archbishop of Armagh. Cullen's successor in Dublin, Archbishop Edward McCabe was also made a cardinal. After that however, the red hat (ie, being made a cardinal) was invariably awarded to the Roman Catholic Archbishop of Armagh, until in a considerable surprise Pope John Paul II awarded the red hat not to the low-key pastoral Archbishop Sean Brady of Armagh, but to the higher profile more intellectual and openly conservative Archbishop Desmond Connell in Dublin. That Dublin, not Armagh will continue to be treated as de facto the premier See was shown in 2003 in the selection of Diarmuid Martin, a noted Vatican diplomat tipped in his own right to receive a red hat, to be Connell's replacement in Dublin.
The partition of Ireland in 1920 in effect gave the Primate of Ireland and Primate of All Ireland differing roles, given that each is based in a different part of the divided island, the former in the south, the latter in Northern Ireland. As a result the Primate of Ireland has effectively become the head of the Church in the Republic of Ireland, while the Primate of All Ireland is the head of the Church on the island of Ireland.
1 That does not mean there have not been more than one Irish person in the College of Cardinals. Irish Archbishops based in the Vatican have been awarded the red hat alongside Irish-based Irish Archbishops. In addition, since Pope Paul VI introduced a mandatory retirement age at which point cardinals cease to have a vote in the College of Cardinals, Ireland has had the experience of having two diocesan cardinals; a reigning cardinal, Desmond Cardinal Connell, Archbishop of Dublin, and a retired cardinal, Cathal Cardinal Daly, former Archbishop of Armagh. Given that Connell's retirement is imminent, the question arises as to whether, with two retired cardinals, neither with votes at the papal conclave, a third red hat might be offered, more probably to Archbishop Martin of Dublin than Archbishop Brady of Armagh.Footnote