The "back story" to Pope Paul's action is somewhat involved. The schema that eventually became Chapter 8 of Lumen Gentium did originally include the title "Mother of the Church" in its title. It was removed by the Theological Commission of the Council (cf O'Malley's What happened at Vatican II p.246 and Wiltgen's The Rhine flows into the Tiber p.240). Debate on the Council floor included interventions in favour of the title and interventions against its adoption. Pope Paul's own feeling in favour of the title had been expressed at the closing of the previous, second session of the Council (Italian text here, cf n.21), when he had explicitly expressed the hope that the Virgin Mary could be given the title in view of the consideration of the nature of the Church that was so much a part of the work of the Council. His affection for the title was articulated again in the Apostolic Exhortation Signum Magnum in 1967, an Apostolic Exhortation which develops the meaning of the title in some detail.
Much of the discussion at the Council surrounding the title and the schema on the Virgin Mary appears to have been in terms of the potentially adverse ecumenical implications of the adoption of any new titles, but hindsight suggests that this was to rather miss the point. Indeed, the title "Mother of the Church" seems to have had precedent in the life of the Church both recent and more distant - Paul Haffner's treatment in The Mystery of Mary, for example, cites Irenaeus, Ambrose, Augustine, Anselm and Rupert of Deutz using terms that implicitly, through recognising the Virgin Mary as mother of the grace, mother of us all, and the like, indirectly recognise her as Mother of the Church. Papal precedent is also cited from Pope Benedict XIV, John the XXIII and now Paul VI. And there is the lovely, short passage in Cardinal Journet's Theology of the Church, published in French in 1958, within five years of the opening of the Second Vatican Council, a passage whose spirit can very much be seen in the work of Hans Urs von Balthasar/Adrienne von Speyr and others:
... Mary is, in the Church, more a Mother than the Church, more a Bride than the Church, more a Virgin than the Church. We mean that she is Mother, Bride, Virgin prior to the Church and for the Church; that it is in her, above all, and by her that the Church is Mother, Bride and Virgin. It is by a mysterious excellence that is diffused from Mary that the Church can truly be, in her turn, Mother, Bride and Virgin. In the order of the grandeurs of sanctity, which are the supreme grandeurs, Mary is, around Christ, the first wave, as it were, of the Church, the genetrix of all others, until the end of time.How can we characterise Pope Paul's action in proclaiming the title of Mary as "Mother of the Church"? One can perhaps see in Pope Paul's affection for the title "Mother of the Church" a particularly vivid experience of this ecclesial heritage, and a wish to proclaim it anew to the Church of his own times. I wonder, though I have no way of knowing just how far it is true, if there is not at least a hint of an immediate intervention of the Holy Spirit that guided Pope Paul's action. (Perhaps that is a question that might be explored by those who might write an academic study Pope Paul's life and ministry in the light of the forthcoming beatification.).
Some see Pope Paul's action as being a deliberate one in which he asserted his own, proper, apostolic authority, vis-à-vis the Council, by insisting on a title that the Council itself had chosen, by whatever course of events, not to take up. However, a footnote in O'Malley's What happened at Vatican II suggests another insight. The footnote is about the events leading up to this action by Pope Paul and reads in part:
For a lengthy analysis, see Rene Laurentin, "La proclamation de Marie 'Mater Ecclesiae' par Paul VI: Extra concilium mais in concilio (21 novembre 1964)""Outside the Council" but "in council" loses something of the nuance of the original phrasing. But Laurentin is surely right to suggest that, though it was an action taken outside the immediate work of the Council, it nevertheless retains a very strong relation to the Council.