You are placing Peter and Paul in competition with Christ, that's false. Christianity spread through the Jews and the Gentiles through word of mouth as there was as yet no Scripture beyond the OT, this is the oral tradition that precedes the NT. The Spirit does not exist in a vacuum, nor does the Spirit dictate. Peter and Paul, both filled with the Spirit, had differences as do the thousands of denominations today who all claim to be led by the Spirit of Christ.
That could have been copied and pasted from a book or even learned off by heart from another's teachings.
It does no such thing, as suggested by yourself.
You see Christ, Peter and Paul did everything to the Glory of God.
Had you been taught by God and not man, then you would have understood that they worked to the Glory and praise of God.
There is still not scripture beyond the OT. Christ having fulfilled all that was written about himself in the Law and the Prophets,
For they shall be taught of God.
King James Bible
And all thy children
shall be taught of the LORD; and great
shall be the peace of thy children.
King James Bible
And they shall teach no more every man his neighbour, and every man his brother, saying, Know the LORD: for they shall all know me, from the least of them unto the greatest of them, saith the LORD: for I will forgive their iniquity, and I will remember their sin no more.
John:16:13
13 Howbeit when he, the Spirit of truth, is come, he will guide you into all truth: for he shall not speak of himself; but whatsoever he shall hear, that shall he speak: and he will shew you things to come.
1 John 4
4 Beloved, believe not every spirit, but try the spirits whether they are of God: because many false prophets are gone out into the world.
2 Hereby know ye the Spirit of God: Every spirit that confesseth that Jesus Christ is come in the flesh is of God:
1 john 2.
27 But the anointing which ye have received of him abideth in you, and ye need not that any man teach you: but as the same anointing teacheth you of all things, and is truth, and is no lie, and even as it hath taught you, ye shall abide in him.
The NT was showing the fulfillment of the OT and how believers would be and were taught by God.
If you do not have the Spirit then you do not belong to God. As Christ said.. " Not all who call me Lord, Lord."
There is not set of rules or regulations but the simple truth of believing God and what he has told us about his son just as Abraham believed what God promised about his Son.
Christ did everything to Gods Glory and Peter like Paul and all who are born of the Spirit have done the same.
You cannot earn it...good works or by how you live... one way... the truth about Jesus Christ who tells us to love God and others with all our hearts.
I believe that is what is meant by Christ teachings in the bible. If you think it is wrong then please discuss.