Of course, everyone knows that modern Protestantism holds to sola scriptura (SS), the idea that the Bible alone is the final and ultimate source of authority for right belief and right practice; orthodoxy and orthopraxy, respectively. Part of the problem of intelligently debating SS is that there are so many different flavors of it. There are those who hold that everything we say we believe or do in worship must be explicitly sanctioned by Scripture. There are others who believe that as long as something isn't explicitly prohibited, then its fine. Diverse groups have diverse understanding of the specific content of this doctrine, but ultimately I think it is safe to say that, for a Protestant, if it can't be proven from the Bible, then it must be rejected.
You can't prove sola scriptura from the Bible!
Which brings me to my first problem with SS; it is internally inconsistent. The Bible does not say that the Bible alone is to be our ultimate source of authority. There are verses that support the authority of the Bible - like Hebrews 4:12 or 2 Timothy 3:16 - but these do not preclude other sources of authority. No verse says "scripture alone" and if we examine the historical evidence, it is clear the early church was not SS. First, the Judaism from which Christianity sprang was not SS as it regards the Torah and prophetic writings. They accepted and eventually codified in writing the oral tradition which authoritatively interpreted the text. That is not to say there wasn't ongoing debate, but it is clear that the rabbinic intepretations were considered normative. The church of the first few decades continued to meet in the synagogues & Temple, followed the Jewish liturgical calendar and pattern of worship (excepting only the Eucharist, which was held in people's homes at first) and the Jewish pattern of thinking. Second, the history of the first 2 centuries shows that the church functioned quite well without a defined canon. Instead, it relied on the Apostolic Tradition which was supplemented by various writings. Some of these writings were eventually put in the canon and some weren't. No matter what texts they were using, the Tradition still functioned as a legitimate and normative authority upon which they relied. Thus, the early church was not SS, and indeed could not have been without a canon. And if those closest to the Apostles did not adhere to what would have obviously been a very important (if impossible) principle, then one can safely conclude that the Apostles did not intend the church to follow it.
Which brings me to a second major inconsistency - the Bible never gives us a definitive list of the canon (most scholars agree the "table of contents" section in the earliest manuscripts were later additions). Protestantism would hold that our faith rests solely on the Bible; B=>F, if you will. But the reality is that with no definitive, self-contained canonical descriptions, the Bible rests on the authority that declared it to be the canon, A=>B. This puts Protestantism in the implicit position of affirming A=>B=>F, or A=>F. 'A' is by definition external to the Bible, and cannot be proven from it in violation of SS. The matter is further complicated by the New Testament's internal references to the Old Testament - they largely quote the Septuagint, which raises the question of which version of the OT the Apostles regarded as authoritative. Can the Protestants sole reliance on the Masoretic text be justified in light of this? And what about NT citation of an apocryphal work - what is the status of that work? Those questions can only be answered from outside the Bible. Regardless if the authority is history, a church council or personal judgment, those questions require an authority quite apart from the Bible to determine what the Bible is. That authority then becomes the ultimate arbiter of faith because it is what delimited the content of the canon.
So how was the canon formulated? The specifics are not as important to this discussion as the general ideas behind what are really the only 2 possibilities; the canon was formulated under the guidance of the Spirit or it relied solely on human judgment. The obvious problem with reliance on human judgment is that it is fallible. I have seen some courageous souls who will allow that they have a "fallible collection of infallible books", but they can't really say that and mean it. If it is a "fallible collection", then it is entirely possible that something 'uninspired' made it in and something 'inspired' was left out, and there is no way for us to ever know if this is the case. One cannot prove that James is uninspired, as some of the Reformers thought, and that the Epistles of Clement are inspired, as some of the Church Fathers thought. This, of course, throws SS into some murky waters - how can you consider a fallible canon to be the ultimate authority for matters of faith? What if you're relying on an uninspired work for some key pieces of your theology or praxis? Here, the authority the faith is really resting on is the mental acuity and historical awareness of a group of very fallible men, which does not strike me as a very strong foundation. Moreover, when you consider that, as I've pointed out previously, Protestantism largely considers these men to have slipped into the serious failures of monepiscopacy, sacramentalism, Traditionalism, etc, I fail to see how anyone could NOT question their wisdom and judgment in this matter. Especially when you consider they came to these positions while reading these texts! If they got it all so wrong in other important areas, why should we think they'd do any better here? This position has to inject some doubt into the validity and completeness of the canon.
But what if the formulatoin of the canon was directed, in some way, by the Holy Spirit? This would give us great assurance that our canon is valid and complete, but once again, it is a violation of SS; you cannot prove from the Bible that the canon was inspired by the Spirit. Another problem also arises, in that if the Protestant accepts the Spirit's guidance here then he must give an account as to why the Spirit did not similarly act to prevent the fledgling church from falling into these heretical, unbiblical forms.
The doctrine of the Trinity came first.
Things are further complicated for the Protestant SS position by the doctrine of the Trinity. First, the Trinitarian formulation of the first Ecumenical Council significantly predates the official formulation of the canon. With no set canon, one cannot affirmatively say that the doctrine of the Trinity is solely based on the Bible as we know it. It is possible that other works influenced the Council's thinking and the unbiblical word "homoousion" surely prevents a SS understanding of this key doctrine. Second, in the Church's battle with the Arian heresy, as happened with many heresies in the first millenia, it was clear that the heretics were reading the same texts as the Trinitarians. The Council was not able to simply dismiss Arius out of hand as relying on false sources or documents, as they could with some of the gnostic sects. In order to confront and overcome the Arian heresy about Christ, they had to prove that Arius was misinterpreting those texts. The significance of this fact is immense for Protestantism. If it accepts the Trinitarian formulation of Nicea, then it must, in fact, rely upon the exegetical skills of the council members. It must look to the quality of their minds, their theology and their adherence to the historic deposit of faith and hold them above reproach. But this the Protestant cannot do! To do this would require a radical rethinking of Protestant theology, ecclesiology, worship and praxis, because once you allow the superiority of their intellects in producing such a key doctrine, you have no basis to reject their thinking in other matters. This does not mean that one would have to accept modern Catholicism or Orthodoxy, but it would mean having to seriously engage the early church's thinking with the intention of being conformed to it. Further, the Protestant cannot do this because it sets up yet another authority outside the Bible. The validity of their interpretation cannot be proven from the Bible, because Arius was reading the same works! His interpretation, which was actually more popular for a while, is just as legitimate a reading unless one accepts an external authority to contradict it. If one denies that source, then one must reject Nicea and simply say that they choose to accept the doctrine of the Trinity based on their own reading of the text. This kicks the legs out from under any orthodox understanding of the faith. For instance, a Calvinist can look at an Arminian and say they think the Arminian's theology is wrong. But that Calvinist cannot deny their Christianity because they are both orthodox and the matters upon which they differ are, to some extent, optional. However, once you reject Nicea, being Trinitarian must similarly become optional because it is based on some school of thought and not some objective reality.