Paul is the only author in the entire Bible who explains who man is, where he is at, and where he is going. He's the only one who explains sin, what it is, what it means, and how to overcome it.
The message Paul teaches about sin is that it is our nature to sin, but the forgiveness of sin by Grace through faith is not a license to sin, we can overcome sin to the point of it not having dominion over us.
Christ teaching on sin is a totally different thing or reason. Christ was the last prophet under Law, he taught the Law, and at the same time revealed the depth of the Law. He made it totally obvious man cannot keep the Law by trying, man needs help from a higher power. But before the higher power can help, sin must be dealt with, that is what He came to do. He condemned sin in the flesh, and defeated it.
Now through His perfection, BY OUR FAITH in Him, the Law that He kept perfectly is fulfilled in us. Not by the way the Old Testament saints were required to do, but now under Grace, the Law is kept by faith in Christ.
Rom. 8:3-4
"For what the law could not do, in that it was weak through the flesh, God sending his own Son in the likeness of sinful flesh, and for sin, condemned sin in the flesh:
That the righteousness of the law might be fulfilled in us, who walk not after the flesh, but after the Spirit."
Those that "walk not after the flesh" are those have total faith in what Christ did, and allow the Holy Spirit to work in them of His will, not your trying as did those who were under Law.
Suffering is the only remedy for sin!
1 pet 4:1 Forasmuch then as Christ hath suffered for us in the flesh, arm yourselves likewise with the same mind: for he that hath suffered in the flesh hath ceased from sin;
Matthew 10:38
And he that taketh not his cross, and followeth after me, is not worthy of me.
Matthew 16:24
Then said Jesus unto his disciples, If any man will come after me, let him deny himself, and take up his cross, and follow me.
Romans 5:3
And not only so, but we glory in tribulations also: knowing that tribulation worketh patience;
Romans 5:4
And patience, experience; and experience, hope:
Romans 8:17
And if children, then heirs; heirs of God, and joint-heirs with Christ; if so be that we suffer with him, that we may be also glorified together.
2 Corinthians 12:9
And he said unto me, My grace is sufficient for thee: for my strength is made perfect in weakness. Most gladly therefore will I rather glory in my infirmities, that the power of Christ may rest upon me.
2 Thessalonians 1:5
Which is a manifest token of the righteous judgment of God, that ye may be counted worthy of the kingdom of God, for which ye also suffer:
Colossians 1:11
Strengthened with all might, according to his glorious power, unto all patience and longsuffering with joyfulness;
2 Tim 2:3 Thou therefore endure hardness, as a good soldier of Jesus Christ.
2 Timothy 2:12
If we suffer, we shall also reign with him: if we deny him, he also will deny us:
Phil 1:29
For unto you it is given in the behalf of Christ, not only to believe on him, but also to suffer for his sake;
James 1:2-8
My brethren, count it all joy when ye fall into divers temptations; Knowing this, that the trying of your faith worketh patience. But let patience have her perfect work, that ye may be perfect and entire, wanting nothing
Hebrews 6:12
That ye be not slothful, but followers of them who through faith and patience inherit the promises.
Hebrews 10:36
For ye have need of patience, that, after ye have done the will of God, ye might receive the promise.
Hebrews 12:4
Ye have not yet resisted unto blood, striving against sin.
1 Peter 2:20
For what glory is it, if, when ye be buffeted for your faults, ye shall take it patiently? but if, when ye do well, and suffer for it, ye take it patiently, this is acceptable with God.
Romans 8:17
And if children, then heirs; heirs of God, and joint-heirs with Christ; if so be that we suffer with him, that we may be also glorified together.
2 Timothy 2:12
If we suffer, we shall also reign with him: if we deny him, he also will deny us: