The Protestant or Roman Catholic (or other) canon represents very complex arguments that are hard to place in sound-bite format, so it's really an impossible task. In addition, much of what we know and many of the arguments we might reference are, themselves, built upon arguments of others-- however diligent we may be in researching them or crafting them together into reasonable comments.
Here are some observations and remarks I have, though, about the canon.
Point 1: The Canon Argument isn't Catholic v. Protestant only. First of all, technically we know that ‘Protestant’ is a general pejorative tag given to reference non-Catholics, and though I will use it here for the purpose of convention, it should be noted that it isn't technically historically-correct and its pejorative nature is disappointing. Protestantism is a movement that grew specifically out of the 16th Century groups who specifically challenged the weakened religio-political status of the Roman Church. Other non-Catholic groups exist which are not “Protestant.” But for argument-sake, we’ll use the Protestant term.
Here’s why that is important: There was not/are not only two competing views of the canon (i.e., it’s not as if there is a Catholic and a Protestant canon only—multiple canons exist). So one could say that this “either RCC or Protestant” is a classic either-or fallacy… though I happen to accept the dominant prevailing, popularized ‘Protestant’ canon (27 NT, 39 OT inspired books). I share this feature only to clarify the assumptions that are embedded into the question itself.
Point 2: Canonicity Completely Depends on Authority. Different ecclesiastical authorities have spoken as to their understanding of canonical ‘collections.’ Either one assumes that one authority is supreme over the others or that they represent the best perspective those individuals (like Athanasius, Origen, Jerome, Luther, Pius IV, etc.) or those groups (Different Roman Catholic voices over the centuries, Ethiopian Orthodox, the Reformers, the Syrian Church) at the time.
RCC Authority. If the Roman Catholic papacy and the morphing understanding of ‘Holy Tradition’ is considered the only legitimate Apostolic Church, then there is no way to resist the canon the RCC has dictated—regardless of however that body of literature has been, is now, or may be understood in the future. In that sense, their authority would trump any other argument—and that is the strength and the weakness of the RCC canon.
Non-RCC Authority. Authority does exist, but if it is not within the RCC, the authority of Christ must be dispersed in other places in the Body of Christ. The Orthodox make very powerful arguments that, I think, are more compelling than Roman Catholic arguments in many ways. But neither RCC or Orthodoxy establish the case in my mind, however. I believe that authority is not given to a visible body, but to the invisible Body of Christ, represented in the general perspective of committed, godly leaders in the church who accept the authority of Christ and His Word through His Spirit’s guidance. This is more ethereal and lacks the dogmatic clarity of Orthodoxy or Catholicism, but that is not a concern of mine. God has routinely worked outside of an identifiable, visible institution and continues to do so today in many cases.
So… if the self-imposed authority of the RCC papacy is a spurious argument, if Holy Tradition is not without error, and if the RCC is prone to mistakes, then the idea of the Apostolic Succession vested in the Holy See is illegitimate. That is my position with the authority of the RCC. And if the authority of the RCC is ruined, then the authority to “RECOGNIZE THE RECEIVED TEXT” is vested outside the papacy and Councils/Trent. This authority is the invisible church, the universal (Catholic, not Roman) Church.
Point 3: Many Early Lists and Essentially Every Later and Modern List of Canons Published Include the 66 Books Recognized Today. There are numerous historical ‘lists’ of canon that make it difficult to build a cohesive, iron-clad case for one single progression of thought—but the 66 books we understand as canonical have repeatedly been affirmed through the Early Church (from, if my facts are straight, the Synod of Hippo, to Athanasius of Alexandria in 367, forward) up until today.
Point 4: Only at Trent (1564, Pius IV) Were the Apocrypha Affirmed by the Papacy. Though the Vulgate had included the Deuterocanonical books in their Latin version, the fact that it took nearly 16 centuries and a counter-reformation to finally consider them ‘scripture’ is telling. That is what I call really late to the party.
Point 5: The Apocrypha were not cited by Christ or the Apostles. Though the NT quotes the OT some 250+ times, it not once quotes the Apocrypha.
Point 6: Jews Did Not Accept the Authority of the Apocrypha. It’s ironic that the Jewish people and Jewish believers did not ever see fit to recognize those books but 1600-1900 years after the fact, a Roman Catholic meeting would affirm them.
Point 7: Jesus Curiously Excluded the Apocrypha as Authoritative. When Jesus referenced what the scriptures were (prior to the New Testament being written, but centuries after the Apocrypha was written), he excluded it from consideration. Note Luke 24:44, where Jesus did NOT reference the “Law, Prophets, and WRITINGS” which Roman Catholics use to argue inclusion of the Deuterocanonical writings—but, INSTEAD, Jesus refers to the Law, Prophets, and the PSALMS. Quote: "Now He said to them, "These are My words which I spoke to you while I was still with you, that all things which are written about Me in the Law of Moses and the Prophets and the Psalms must be fulfilled.”
Point 8: Jerome, Josephus, Phillip Schaff, and Others Honored the Apocrypha, But Rejected It As Authoritative. Even though they valued its contribution, they did not consider it scripture and canonical—even though Jerome was against its inclusion, he was compelled (forced) to include some of those writings in the Latin Bible, his Vulgate—but most were inserted after his death. Philo, the well-known Hellenistic Jew, apparently didn’t even mention the Apocrypha. I think that’s telling.
Point 9: No Apocryphal Writers To My Knowledge Lay Claim to Biblical Authority.
Point 10: Four Centuries Passed Before They Were Apparently Included In Anyone’s List of Scripture.
Point 11: Some Apocryphal Books Contain Fantastic Statements That Are Contradictory To Divine Scripture and that Cannot Be Historically Accurate. For example, I think that the books of Maccabes include multiple different accounts as to when Antiochus Epiphanes died and was buried. Also, we know that they teach things foreign to scripture like praying for the dead, sinless perfection of saints while on earth, purgatory, etc.
Point 12: Jerome, of the Vulgate, Was The First To Use The Word Apocrypha. The Word MEANS “Doubtful Authorship.” Authorship of scripture is one of the primary tests of canonicity—so the very fact that the authorship of these books were questioned showed their authenticity as spurious and not apostolic.
Point 13: If the Apocrypha Were Scripture Then They Would Allegedly Include Divine Statements Given During the 400 Years of Silence When God Was Not To Be Speaking. To me, that’s devastating to such an argument for the Apocrypha.