1. It's Not Taught in the Bible

Scripture certainly is a “standard of truth”, but not in a sense that rules out the binding authority of authentic apostolic tradition and the Church. Catholics agree with Protestants that Scripture is materially sufficient: i.e., every true doctrine can be found in the Bible, if only implicitly and indirectly by deduction. But no biblical passage teaches that Scripture is the sole rule of faith for the Christian (formal sufficiency). Nor can sola Scriptura be deduced from implicit passages.

2. “Word of God”

“Word” in Holy Scripture quite often refers to a proclaimed, oral word of prophets or apostles. They spoke the word of God, whether or not their utterances were later recorded in Scripture (see, e.g., Jer 25:3, 7-8). The oral “word” had equal authority. This was also true of apostolic preaching (1 Thess 2:13).

3. Tradition is Not a Dirty Word

The Bible condemns corrupt traditions of men (e.g., Matt 15:2-6, Mk 7:8-13, Col 2:8). Catholics agree with this. But it’s not the whole truth. True, apostolic traditions are also positively endorsed. These traditions are in total harmony with and consistent with Scripture. In that sense, Scripture is the “final judge” of tradition, but not in the sense that it rules out all binding tradition and Church authority (see, e.g., Acts 2:42; 1 Cor 11:2; 2 Thess 2:15; 2 Tim 1:13-14; 2:2; Jude 3).

4. Jesus and Paul Accepted Non-Biblical Oral and Written Traditions

Jesus and St. Paul accepted the authority of the Old Testament, but they also appealed to other authority, outside of written revelation. For example, in Matthew 23:2-3, Jesus teaches that the scribes and Pharisees have a legitimate, binding authority, based on a teaching succession from Moses’ seat, which phrase (or idea) cannot be found anywhere in the Old Testament. It is found in the (originally oral) Mishna.

In 1 Corinthians 10:4, St. Paul refers to a rock which “followed” the Jews through the Sinai wilderness. The Old Testament says nothing about such miraculous movement, in the related passages about Moses striking the rock to produce water (Exodus 17:1-7; Numbers 20:2-13). But rabbinic tradition does. Paul refers in 2 Timothy 3:8: to “Jannes and Jambres” who  “opposed Moses”. These two men cannot be found in the related Old Testament passage (Exodus 7:8 ff.), or anywhere else in the Old Testament.

5. Jerusalem Council

The Jerusalem Council (Acts 15:6-30) made an authoritative pronouncement (citing the Holy Spirit) which was binding on all Christians (Acts 15:28-29). In the next chapter, we read that Paul, Timothy, and Silas, traveling around, “delivered to them for observance the decisions which had been reached by the apostles and elders who were at Jerusalem” (Acts 16:4).

6. Pharisees, and Oral, Extrabiblical Tradition

Christianity was derived in many ways from the pharisaical tradition of Judaism (which accepted oral tradition). Christian Pharisees are referred to (Acts 15:5; Phil 3:5), so neither the (orthodox) Old Testament Jews nor the early Church were guided by the principle of sola Scriptura. The Pharisees (despite their corruptions and excesses) were the mainstream Jewish tradition, and both Jesus and Paul (who called himself a Pharisee three times: Acts 23:6; 26:5; Phil 3:5) acknowledge this.

7. Old Testament Jews Did Not Believe in Sola Scriptura / Necessity of Interpretation

Ezra read the law of Moses to the people in Jerusalem (Neh 8:3). Thirteen Levites assisted him and “helped the people to understand the law” (8:7) and “gave the sense, so that the people understood the reading” (8:8; cf. Ezra 7:6, 10, 25-26; 2 Chr 17:8-9). The New Testament concurs. Philip asked the Ethiopian eunuch, “Do you understand what you are reading?” And the eunuch replied, “How can I, unless some one guides me?” (see Acts 8:27-31). St. Peter states that “no prophecy of scripture is a matter of one’s own interpretation” (2 Pet 1:20), and refers to parts of Paul's epistles being “hard to understand, which the ignorant and unstable twist to their own destruction, as they do the other scriptures” (2 Pet 3:15-16). Likewise, Jesus “explained everything” about the parables to His disciples (Mk 4:33-34).

8. 2 Timothy 3:16-17: The Protestant “Proof Text”

All scripture is inspired by God and profitable for teaching, for reproof, for correction, and for training in righteousness, that the man of God may be complete, equipped for every good work.

This passage doesn’t teach formal sufficiency. In 2 Timothy alone (in context), Paul makes reference to oral tradition three times (1:13-14, 2:2, 3:14). Also, a very similar passage, Ephesians 4:11-15, would prove (using Protestant reasoning) the sufficiency of “pastors” and “teachers” for the attainment of Christian perfection. The Christian believer is “equipped, built up,” brought into “unity” and “mature manhood, knowledge” of Jesus, the “fulness of Christ,” and even preserved from doctrinal confusion by means of the teaching function of the Church. Yet this Pauline passage doesn’t even mention Scripture.

9. Paul Casually Assumes that His Passed-Down Tradition is Infallible and Binding

Paul says that Christians should  “have nothing to do with” (2 Thess 3:14) and “avoid” (Rom 16:17) those who refuse to follow his authoritative (and not yet formally scriptural) instructions.

10. Sola Scriptura is a Radically Circular Position

When Protestants are asked why one should believe in their particular denominational teaching rather than another, each will appeal to the “Bible’s clear teaching”. This is similar to people on two sides of a legal, constitutional debate both saying, “well, we go by what is constitutional, whereas you guys don’t.” But judges and courts are necessary, and their decrees are binding.  Protestantism lacks this element because it appeals to a logically self-defeating principle and a book (which must always be interpreted by human beings). In the end, a person has no assurance or certainty in the Protestant system. Denominationalism and divisions are vigorously condemned in Scripture. The Bible teaches that a “three-legged stool”: Bible + Church + tradition, is necessary to arrive at truth. If you knock out any leg, it collapses.