My venerable Predecessor the Servant of God Paul VI announced one in 1967, to commemorate the martyrdom of Saints Peter and Paul on the 19th centenary of their supreme act of witness. He thought of it as a solemn moment for the whole Church to make “an authentic and sincere profession of the same faith”; moreover, he wanted this to be confirmed in a way that was “individual and collective, free and conscious, inward and outward, humble and frank”. He thought that in this way the whole Church could re-appropriate “exact knowledge of the faith, so as to reinvigorate it, purify it, confirm it, and confess it”. The great upheavals of that year made even more evident the need for a celebration of this kind. It concluded with the Credo of the People of God, intended to show how much the essential content that for centuries has formed the heritage of all believers needs to be confirmed, understood and explored ever anew, so as to bear consistent witness in historical circumstances very different from those of the past.Pope Paul's Profession of Faith, pronounced solemnly as the homily during Mass in St Peter's Square on the feast of Saints Peter and Paul in 1968 was, and remains, a tremendous gift to the Church. It very quickly came to be known by the title Credo of the People of God, and the full text is well worth reading. There is a "back story" to Paul VI's Credo, one aspect of which Paul VI refers to himself in his introductory paragraphs to the Credo, and the other of which has emerged since.
During the year or so leading up to the proclamation of the Credo, the Holy See engaged in a lengthy dialogue with the authors, or at least the representatives of the authors designated by the Dutch Bishops Conference, of what was known as the Dutch Catechism. This catechism had the imprimatur of the Dutch Bishops Conference; it was eventually judged to be inadequate as an expression of Catholic faith by a commission of Cardinals appointed by the Holy See to examine it, in dialogue with its authors. At the time, it was the subject of considerable controversy, and it was to the disquiet caused in the Church by this controversy that Paul VI refers in the introduction to the Credo. Mgr Eugene Kevane's book Creed and Catechetics describes this background (pp.61-71 in my 1978 paperback edition); I have not found an on-line account. Mgr Kevane points out that many of the doctrinal difficulties that can be identified in the text of the Dutch Catechism receive a response in the text of the Credo.
The second aspect of the "back story" relates to the formulation of the text itself. According to the account of this article from the magazine 30 Days, it is to Jacques Maritain that we owe a draft that largely became the text proclaimed by Paul VI. Reading the 30 Days article suggests that Maritain experienced a certain charismatic inspiration for his suggestion that Pope Paul should make a profession of faith akin to the great professions of faith of earlier times in the Church. But there is also a more interesting intuition on Maritain's part, and that is the intuition that anathematic condemnations would not be a sufficient way of responding to the situation of the Church at that time. There is a genius in the Credo of the People of God that combines both a clarity and a firmness of teaching with a beauty of expression, an exercise of the Office of the Successor Peter with a regard for the dignity that belongs to all the faithful. Pope Paul explained at the end of his introductory paragraphs (my italics added):
On this day which is chosen to close the Year of Faith, on this feast of the blessed apostles Peter and Paul, we have wished to offer to the living God the homage of a profession of faith. And as once at Caesarea Philippi the apostle Peter spoke on behalf of the twelve to make a true confession, beyond human opinions, of Christ as Son of the living God, so today his humble successor, pastor of the Universal Church, raises his voice to give, on behalf of all the People of God, a firm witness to the divine Truth entrusted to the Church to be announced to all nations....
To the glory of God most holy and of our Lord Jesus Christ, trusting in the aid of the Blessed Virgin Mary and of the holy apostles Peter and Paul, for the profit and edification of the Church, in the name of all the pastors and all the faithful, we now pronounce this profession of faith, in full spiritual communion with you all, beloved brothers and sons.