The situation of the rites of St. Pius V and Paul VI is the one described in the recent Motu proprio Traditionis Custodes: an impossible cohabitation.
1. In his very recent Motu proprio Traditionis Custodes of July 16, Pope Francis establishes (in Article 1) that “The liturgical books promulgated by Saint Paul VI and Saint John Paul II, in conformity with the decrees of Vatican Council II, are the unique expression of the lex orandi of the Roman Rite.”
2. Various reactions were not forthcoming from the Ecclesia Dei groups. Undoubtedly, the situation of all those who, in order to be attached to the traditional liturgy, did not want to follow Archbishop Lefebvre and the Society of Saint Pius X into an alleged “schism,” or at least into an equally alleged “disobedience,” is likely to become very problematic.
This will no doubt appear, and remain in reality, deeply distressing in the eyes of all those whose consideration stops at the personal good of the members of the said movement, or at least at the immediate practical consequences. The example of the Superior of the District of France of the Fraternity of St. Peter is characteristic in this respect, when he sees in Pope Francis' Motu proprio an “offensive” text, which makes little recompense for the efforts of “obedience” made so far, even going so far as to say that “the Society of Saint Pius X is actually being treated better than we are.”
3. For all that its effects seem to be distressing for and detrimental to people, the Pope’s initiative, however, is not surprising. It even makes sense. And one may well wonder if it were not inevitable. Because the situation of the two rites, that of St. Pius V and that of Paul VI, is indeed that described in the recent Motu proprio Traditionis custodes: a situation of impossible cohabitation on the same plane of liturgical principles.
Beyond factual situations and the infinitely variable state, peaceful or conflicted, that concerns people, there is fundamentally a formal opposition of doctrine between the Mass of St. Pius V and the new rite of Paul VI. The liturgy is a theological place. 
The gap between the two liturgies corresponds to an abyss, which separates two conceptions of the Church and the faith. We can actually measure the extent of this gap by seeing how strongly most episcopates, conscious of their adherence to Vatican II, opposed the initiative of the Motu proprio Summorum Pontificum: even if the traditional rite of the Church was not meant, in Benedict XVI’s intention, to exclude the new rite, its enlargement was often misperceived.
And it is precisely because, beyond a purely juridical non-exclusion, there will always remain an incompatibility and a doctrinal exclusion between the two liturgies. The good intentions of a conservative pope, such as Benedict XVI, are similar to those of a liberal: both nurture the illusion of giving the same right to quote truth and error.
But the intentions of an avant-garde Pope, such as Francis, are of a completely different scope: in his mind, the one and only expression of the lex orandi can only be the Novus Ordo Missae, to the exclusion of the traditional Mass. And in this, Francis is much more logical than Benedict XVI, according to the adage that the law of belief is at the basis of the law of prayer, lex orandi, lex credendi.
If the new belief is that of the Second Vatican Council, the new liturgy, which must correspond to it, can only be that of the New Mass of Paul VI, and not that of the old Mass which is the expression of a doctrine contrary on more than one point to that of Vatican II.
4. This clearly means, among other consequences, that the traditional Mass cannot be made the object—neither for a true Catholic attached to Tradition, nor for a true conciliar attached to Vatican II—of a personal preference or of a choice motivated by a particular theological or aesthetic sensibility.
A person does not “prefer” the traditional Mass to the New Mass, as if the New Mass were only less good or less pleasant. Indeed, the traditional rite of the Mass is the complete and necessary expression of the faith of the Church, as opposed to a new rite which (according to the words of the Brief Critical Examination) departs from it in an impressive way as a whole and in detail.
The traditional rite requires the adhesion of every Catholic, who cannot be content to regard it as the object of a personal preference, for reasons which would be extrinsic to the profession of the Catholic faith, and which would not exclude the legitimacy and intrinsic goodness of the new rite of Paul VI.
5. It is undeniable that, through the Motu proprio of July 7, 2007, Benedict XVI wanted to widen the possibility of celebrating the old liturgy, and that this widening was unprecedented since 1969.
But this pope, because he was only conservative, did not go so far as to make the traditional rite the necessary, ordinary, and common expression of the law of prayer; the ordinary expression of this law has in fact remained that of Paul VI's Novus Ordo Missae.
Benedict XVI only wanted, for the same “lex orandi,” that there should be two expressions, one of which (that of the Mass of St. Pius V) would be extraordinary compared to the other (that of the New Mass of Paul VI).
Benedict XVI therefore introduced into the Church's liturgy the impossible dualism of a bi-ritualism, an impossible dualism at the very level of liturgical principles, and this is why his Motu proprio was, in short, only the act of an equally impossible and illusory liberalism, which could satisfy neither the Society of Saint Pius X nor the unconditional advocates of Vatican II, both attached to their principles.
Conservatives of different tendencies, and among them supporters of the Ecclesia Dei movement, saw it as a providential means of reconciling their attachment to the liturgy of St. Pius V and their submission to the teachings of the Second Vatican Council. But now Francis's recent initiative has reminded them that this unstable situation was only made possible for them thanks to the overall personal and ultimately strategic initiative of a conservative pope.
6. Towards all of these people, a Catholic worthy of the name should feel a true compassion: a compassion which is not saddened only about the grave threat against the possibility for these conservatives to celebrate the liturgy of St. Pius V, but also a compassion which is saddened much more by the deadly illusion in which these Catholics risk remaining prisoners, that of believing in the possibility of reconciling the old liturgy and adherence to the Second Vatican Council—or an alleged “obedience” to the current hierarchy.
To all of these, it is important to make people understand above all, with all the pastoral charity we can muster, that the Society of Saint Pius X, no more than the Mass of Saint Pius V, cannot represent either a default option, or an opportune and provisory preference in the present state of the Church.
7. Francis's initiative has the potential to open people’s eyes, and not just their hearts.
Fr. Jean-Michel Gleize
1. Just before the publication of Benedict XVI's Motu proprio, Dom Jean-Pierre Longeat wrote “The Unity of the Roman Liturgy in Question” for the newspaper La Croix on Monday, October 23, 2006. “The 1969 Ordo missae implements in particular the theology of the dogmatic constitution on the Church. Lumen gentium presents the Church both as the Mystical Body of Christ and as the People of God united in the name of Christ. … To want to encourage in the Latin Church the return to another theological emphasis by extension of the 1962 Ordo, will generate a very deep disturbance in the people of God.”