"ALL SCRIPTURE is given by inspiration of God, and is profitable for DOCTRINE, for REPROOF, for CORRECTION, for INSTRUCTION IN RIGHTEOUSNESS: That the man of GOd may be PERFECT, THOROUGHLY FURNISHED unto all good works." 2 Tim. 3:16-17.
Now, would you explain to me why the CC needs something more then PERFECT, THOROUGHLY FURNISHED? John 5:37-40 37And the Father who sent me has himself borne witness about me. His voice you have never heard, his form you have never seen, 38and you do not have his word abiding in you, for you do not believe the one whom he has sent. 39 You search the Scriptures because you think that in them you have eternal life; and it is they that bear witness about me, 40yet you refuse to come to me that you may have life. Jesus always appealed to the written Word of God to settle disputes, never to oral tradition. When He refers to the 'Word of God', His reference is always to recorded Scripture. According to His teaching, Scripture was the final judge of all tradition. In fact, Jesus has virtually nothing positive to say about tradition (cf. Matthew 4:4; 5:17-19; 15:2-9; 22:29-32). Clearly, if the Son of God teaches that all tradition is to be judged by its conformity to the Scriptures, then tradition is subordinate to Scripture and Scripture is logically the ultimate authority.
Then there is Paul commending the Bereans for “searching the scriptures daily to see if these things are true” when speaking of even his teaching.
"But there are also many other things which Jesus did; which, if they were written every one, the world itself, I think, would not be able to contain the books that should be written." John 21:25
"Faith then cometh by hearing; and hearing by the word of Christ." Romans 10:17
"Now I praise you, brethren, that in all things you are mindful of me: and keep my ordinances as I have delivered them to you." 1 Corinthians 11:2
"Therefore, brethren, stand fast; and hold the traditions which you have learned, whether by word, or by our epistle." 2 Thessalonians 2:15
"And we charge you, brethren, in the name of our Lord Jesus Christ, that you withdraw yourselves from every brother walking disorderly, and not according to the tradition which they have received of us." 2 Thessalonians 3:6
"But if I tarry long, that thou mayest know how thou oughtest to behave thyself in the house of God, which is the church of the living God, the pillar and ground of the truth." 1 Timothy 3:15
"Hold the form of sound words, which thou hast heard of me in faith, and in the love which is in Christ Jesus." 2 Timothy 1:13
"Understanding this first, that no prophecy of scripture is made by private interpretation." 2 Peter 1:20
"As also in all his epistles, speaking in them of these things; in which are certain things hard to be understood, which the unlearned and unstable wrest, as they do also the other scriptures, to their own destruction." 2 Peter 3:16