A long quote, but worthy of being shared given the subject matter:
…it is not necessary for anyone to demonstrate that the Missal of Paul VI abrogated the missal that was in force from 1962 to 1969, because this is clear according to common liturgical law. It is up to those who would argue otherwise to provide the proof to support it. As long as they do not offer reasonable arguments of a juridical or liturgical nature, as long as the “double contemporary form” is only affirmed, but not demonstrated and proven, the general principle must be presumed: the new Roman Rite substitutes the older Roman Rite, and a conflict cannot replace the simple fact that only one rite, only one form, and only one use is in force, according to the principle of common law (not to mention common sense).
To that we can add, to be thorough, another consideration. Not only is it impossible to deduce from the text of Sacrosanctum Concilium some parallel existence of two ritual forms in force in the single Roman Rite; in fact, such an idea clearly runs contrary to the conciliar text, which indicates clear intentions of revision and substitution of the preconciliar liturgy. Indeed, a great many implementing measures of the reform, promulgated by Pope Paul VI, demonstrate a clear intention to substitute the older ritual regime with the newer one (as has been the case throughout the history of the church). Furthermore, one can even recognize such an intention in Paul’s predecessor, John XXIII, who, in the document that introduces and makes possible the 1962 edition of the Tridentine missal, emphasizes not only the desire to continue (and bring to completion) Pope Pius XII’s project of a complete revision of the rubrics of the Breviary and of the Roman Missal but of doing so for the period of time – still difficult to foresee in 1960 – until the convocation of the Second Vatican Council and the work of liturgical reform it was expected to accomplish. It should not surprise us, then, that the Missal of 1962 – the very one that is today claimed to have force sine die alongside the one approved by Pope Paul VI – was approved by Pope John XXIII as a “provisional text” in expectation of the Council and of the liturgical reform that was in 1960 already expected to result from it.
The nonabrogation of the Missal of Pius V, then, means little. Supporting such a central and decisive affirmation with an argument from silence – together with the fact that two preceding popes (one could even say three, since, as we have seen, one could also include John XXIII) each understood the postconciliar rite as the only one effectively in force, making exception to this case by the use of indult – raises an objective and urgent problem that must be clarified in some other way, in order not to leave a grave uncertainty that would influence reasoning and practice on related matters.
Andrea Grillo, Beyond Pius V: Conflicting Interpretations of the Liturgical Reform, trans. Barry Hudock, Rev. Ed. (Collegeville, MN: Liturgical Press, 2013), pp. 107-109. ISBN: 978-0-8146-6327-1.