Today during the Sunday Angelus, a Sunday which is also the Feast of the Cathedral of Peter, the Holy Father made pointed comments relevant, I believe, to the debate going on about the eventual reconciliation of the SSPX and whether there can be differences within the Church.
This Sunday there also falls the Feast of the Cathedra of St. Peter, an important liturgical recurrence which highlights the ministry of the Successor of the Prince of the Apostles. The Cathedra of Peter symbolizes the authority of the Bishop of Rome, called to perform a distinguishing service with respect to whole People of God.
Immediately after the martyrdom of Sts. Peter and Paul, the Church of Rome was recognized to have the primatial role in the whole Catholic community, a role already attested in the second century by St. Ignatius of Antioch (Ai Romani, Pref.: Funk, I, 252) and by Saint Irenaeus of Lyon (Contro le eresie III, 3, 2-3).
This unique and specific ministry of the Bishop of Rome was reaffirmed by the Second Vatican Council: [I am adding the Latin and giving a standard English translation of the Council citation] [Inde etiam in ecclesiastica communione legitime adsunt Ecclesiae particulares, propriis traditionibus fruentes, integro manente primatu Petri Cathedrae, quae universo caritatis coetui praesidet (Cf. S. IGNATIUS M., Ad Rom, Praef.: ed. FUNK, I, 252.), legitimas varietates tuetur et simul invigilat ut particularia, nedum unitati noceant, ei potius inserviant.]
"Moreover, within the Church particular Churches hold a rightful place; these Churches retain their own traditions, without in any way opposing the primacy of the Chair of Peter, which presides over the whole assembly of charity (Cfr. S. Ignatius M., Ad Rom., Praef.: Ed. Funk, I, p. 252.) and protects legitimate differences, while at the same time assuring that such differences do not hinder unity but rather contribute toward it."
Dear brothers and sisters, this feast offers me the occasion to ask you to assist me ["accompagnarmi"] with your prayers, so that I can accomplish faithfully the profound responsibility Divine Providence has entrusted me as the Successor of the Apostle Peter.
The Pope said that, because he is Peter, he lifted the excommunications of the SSPX bishops in the service of the unity of the Church.