An "important step" was taken when Archbishop Pozzo made a previous declaration that "certain texts of the Council did not constitute criteria for Catholicity." Among these, he said, are texts related to religious freedom, relations with non-Christian religions, ecumenism, and liturgical reform.
"If we were able to determine that this is the line of the whole Church and not of one person or another, that would be decisive," he said, but cautioned that there are still several "red lines" the Society isn't yet willing to cross.
These lines, he said, are drawn when it comes to documents outlining "the way in which ecumenism is practiced, including statements very dangerous for the faith, that make you think all have the same faith; the liturgical question or the relationship between the Church and the State."
"All these are issues on which we will not yield. This is not a matter of a position or personal point of view, or only peculiar to our congregation," he said, adding that the Society upholds "what the Church has already taught and defined on those issues."
"We could summarize by saying that the conditio sine quae non (condition without which it is not) is that Rome accept us the way we are."
Bishop Fellay noted that another point that makes unity difficult the fact that there is currently "a deep division in the Church between conservatives and progressives, which reaches to the highest levels."
"In a certain measure, we are the victims of this dispute, since the official declaration for our communion with the See of Peter will hardly be satisfactory for both positions," he said, but noted that while it's hard to place a date when reconciliation will take place, Rome seems to be more open to a public recognition of "our status as Catholics."
Responding to labels frequently associated with the Society such as "ultraconservative" and "sectarian," Fellay said that if a person wants to "disqualify" the SSPX with these labels, "then you have to condemn the entire Catholic Church, throughout its entire history."
"We simply follow and apply what was practiced by the Church in the entire world for centuries," he said, but noted that while "they wanted to change the Church" in both the pre and post Council era, "we did not abandon the rich heritage of our Holy Mother the Church."
"This simple fact is enough to give us a conservative look," he said, adding that the Society's attempts to "defend and protect" themselves from these type of attacks since the 1970s have been "misunderstood."
Bishop Fellay also said that despite ongoing points of division, the process of unification has sped up under Pope Francis. While things began with St. John Paul II and continued with Benedict XVI, who played "a very important role," it seems that "the most important steps were taken in Francis' pontificate."
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Noting the uptick in priestly vocations within the SSPX, Fellay said what makes their understanding of the priesthood unique is "the spirit of the sacrifice of the Cross, of the sacrifice of the altar, which the priests renews in intimate union with Our Lord, and with which he must identify himself."
In his interview, Archbishop Pozzo said that when it comes to the question of Vatican II, "it's a false problem to ask if a Catholic can accept the Council or not."
"A good Catholic cannot reject it," he said, "because it is a universal assembly of bishops gathered around the Pope."
The real problem, then, is with the interpretation of conciliar documents. Pointing to an idea that came from Benedict XVI, Archbishop Pozzo said the correct interpretation is that the documents be read "one in the line of renewal in continuity with tradition."
"Vatican II must be understood and read in the context of the tradition of the Church and of her constant magisterium," he said, but stressed that "the magisterial authority of the Church cannot stop in 1962."
"Neither is the magisterium above the Word, written or transmitted, nor progress, in the best understanding of the mysteries of faith," he said, adding that teachings of the Vatican II "have a different degree of authority, which corresponds to a different degree of adherence."