I have a major soft spot for Lutheranism because I was baptized Lutheran and its positions so frequently match early patristic ones, like on the Real Presence. This draws me to consider and evaluate one of its foundational dogmas or axioms, "Sola Scriptura."
Luther and the Lutheran Church who created the Sola Scriptura concept defined it in their writings like the Formula of Concord to mean that the Bible Alone is the Only rule and authority:
Accordingly, one would not also use other sources outside the Bible like early Christian writings or Church Councils to help decide on teachings. It's a nicely convenient idea to imagine that we have a single text alone that addresses all religious questions. It also is a convenient way to avoid being forced into the tons of extrabiblical Catholic teachings of the Magisterium.
But the Lutheran and Reformed dogma of Sola Scriptura appears disprovable in both logic and practice. Following the dogma of Sola Scriptura, one should use the Bible alone to judge whether to use the Bible alone. When we turn to the Bible alone to judge this question, we find passages on tangential topics: It says that all Scripture is inspired and it commends early Christians for following the apostles' "traditions." At one point Paul writes in a Biblical epistle that women should wear head coverings and not have authority over mean, and says that his teaching on the topic, which cover numerous verses, is not inspired. However, the Bible alone never specifically says that the Bible alone is the only rule or authority to decide all teachings.
In fact, the Bible gives lots of suggestions to use other helpful sources and materials in addition to judge questions. For example, John's Gospel noted that Jesus gave sayings that were not recorded in the Bible, and the Bible notes that the apostles appointed overseers or bishops over the Christian community. One of the first bishops was Clement of Rome whom Paul mentions. Early writings like II Clement have sayings by Jesus outside the Bible. If you were living in the mid-1st Century, Jesus' sayings and the decisions by apostles and bishops would have some rulemaking authority for you, even if they were neither written in the Bible nor infallible decisions.
The early Church responsible for the Bible must not have wanted and intended for the Bible to be the only authority for Christians because they would have said so in it. The Torah has many detailed prohibitions like avoiding mixing wool with linen. Naturally, if they wanted Christianity to teach such a foundational Lutheran idea as Sola Scriptura, they would have written something like "Scripture is the Only rule" or "never use any authority outside Scripture." Nor does it even claim to cover all religious questions.
Then there is the practical problem. If Sola Scriptura was correct, a faithful person or community could just read the Bible alone and would reasonably find the Bible's position on every issue from it. But in practice, if sincere individual Christians or their groups go by the Bible Alone, they don't understand what its writers intended on all issues. If you give a Bible to a person or group who were never taught anything about Christianity, whether they are tribal people in Africa or young college educated European or Chinese inquirers, they are de facto not going to choose the right answer to every major religious question from Trinitarianism to the Real Presence to Infant baptism.
Second, the Sola Scriptura denominations, from Lutherans to the Amish to Baptists to Calvinists, disagree on what the Bible teaches on such major issues as having bishops, baptizing infants, and the objective Real Presence in the elements. Each one may believe that they have found the Biblical position by reading the Bible alone and that all other Bible-Only believers are wrong. But objectively and practically speaking, if the Bible Alone were the right, correct approach for faithful Christians, then they would not read it and come to so many opposite conclusions on so many questions so frequently.
