Why would Paul pass something on by word of mouth that contradicted what he wrote in his letters?
Now you're claiming from scriptural authority that scripture alone isn't authoritative. If it's not authoritative, why should I believe your claim that scripture isn't authoritative?
The church was built on the foundation of the apostles and prophets: "So then you are no longer strangers and aliens, but you are fellow citizens with the saints and members of the household of God, built on the foundation of the apostles and prophets, Christ Jesus himself being the cornerstone, in whom the whole structure, being joined together, grows into a holy temple in the Lord."—Ephesians 2:19-21
If the foundation has already been laid on the apostles and prophets, how can another foundation be laid? Every book of the New Testament was written by an apostle or an associate of an apostle. It is the record of the apostles' teaching and of the oral tradition that was handed down by them.
Don't reject what I'm saying before thinking about it carefully. Don't react without considering the logic in it.
You ask, "Why would Paul pass something on by word of mouth that contradicted what he wrote in his letters?" I never said that he contradicted what he wrote in his letters. But it's very clear from what he is saying that he taught both orally and in writing and his oral teachings and the teachings of the church were not put down in writing. And, even if they weren't put down in writing Paul demands that Christians be true to both oral and written teaching, even if the oral teaching didn't end up in the bible.
And, you gotta remember that less than 1% of the people were literate,, they couldn't read so they had to be taught orally. Even well past the time of Gutenberg's printing press the great majority of people were illiterate.
And there wasn't even a bible until 300 years after Christ ascended to heaven. So you bet there was a lot of oral teaching going on.