You completely ignore the rest of the verse:
"and is profitable for doctrine, for reproof, for correction, for instruction in righteousness, that the man of God may be perfect, throughly furnished unto all good works."
This states quite clearly that by scripture, man is thoroughly and completely equipped for all good works.
The Bible denies that it is sufficient as the complete rule of faith.
Amazing - if you think the inspired word of God is not sufficient for your faith and salvation and you feel that you need to add to it, then I am sorry and afraid for you.
Paul says that much Christian teaching is to be found in the tradition which is handed down by word of mouth (2 Tim. 2:2). He instructs us to "stand firm and hold to the traditions which you were taught by us, either by word of mouth or by letter" (2 Thess. 2:15).
Where do you think Paul got those "traditions"? Do you think he just made them up and that they are extra-biblical? The Bereans are commended in Acts for checking everything that Paul said to verify that it conformed to scripture:
Acts 17:10-11
And the brethren immediately sent away Paul and Silas by night unto Berea: who coming [thither] went into the synagogue of the Jews. These were more noble than those in Thessalonica, in that they received the word with all readiness of mind, and searched the scriptures daily, whether those things were so.
If Paul had told the Bereans that they could pay or pray their relatives out of some place called purgatory they would have searched the scriptures and told him he was wrong - first that there's no purgatory and secondly that the only payment for sin is the blood of the perfect sacrifice Jesus Christ.
This oral teaching was accepted by Christians, just as they accepted the written teaching that came to them later. Jesus told his disciples: "He who hears you hears me, and he who rejects you rejects me" (Luke 10:16). The Church, in the persons of the apostles, was given the authority to teach by Christ; the Church would be his representative. He commissioned them, saying, "Go therefore and make disciples of all nations" (Matt. 28:19).
As pointed out above, this oral teaching must always be in accordance with scripture.
And how was this to be done? By preaching, by oral instruction: "So faith comes from what is heard, and what is heard comes by the preaching of Christ" (Rom. 10:17). The Church would always be the living teacher. It is a mistake to limit "Christ’s word" to the written word only or to suggest that all his teachings were reduced to writing. The Bible nowhere supports either notion.
As stated above, this oral teaching must always be in accordance with scripture. Also, you have misquoted Romans 10:17. The correct translation is: So then faith [cometh] by hearing, and hearing by the word of God. The "word of God" is plainly a reference to scripture. What translation are you using? Also, if you believe that the church is a "living teacher" in the sense that liberals believe the Constitution is a "living, breathing document", I completely reject that notion, otherwise we are simply allowing for all sorts of erroneous, unscriptural doctrine of men to be presented as God's word.
Further, it is clear that the oral teaching of Christ would last until the end of time. "’But the word of the Lord abides for ever.’ That word is the good news which was preached to you" (1 Pet. 1:25). Note that the word has been "preached"—that is, communicated orally. This would endure. It would not be supplanted by a written record like the Bible (supplemented, yes, but not supplanted), and would continue to have its own authority.
So you feel that the Bible is merely supplemental to oral tradition? Wow, that is totally contrary to what the Bible itself teaches. Let me guess, you must be a Mormon or Jehovah Witness. Once again, your translation differes significantly from the King James, which reads: "But the word of the Lord endureth for ever. And this is the word which by the gospel is preached unto you."
This is made clear when the apostle Paul tells Timothy: "[W]hat you have heard from me before many witnesses entrust to faithful men who will be able to teach others also" (2 Tim. 2:2). Here we see the first few links in the chain of apostolic tradition that has been passed down intact from the apostles to our own day. Paul instructed Timothy to pass on the oral teachings (traditions) that he had received from the apostle. He was to give these to men who would be able to teach others, thus perpetuating the chain. Paul gave this instruction not long before his death (2 Tim. 4:6–8), as a reminder to Timothy of how he should conduct his ministry.
If there was something so important that it needed to passed down the "apostolic chain" to today, don't you think Paul would have written it down? Why would he leave it to chance? This supposed perpetuated chain of oral tradition is simply a way for extra-biblical, non-scriptural teachings to be passed off as doctrine, something that a Berean would point out immediately.
I pray that if you are a part of a church that teaches such things, that you will seriously consider examining everything with scripture, as the Bereans were commended for doing.