This wasn't a letter to the Jews. It's called Romans. I am sure there were some Jews there, but by now, 30 years after Jesus death and resurrection, people were familiar with why he died, what the Law was, from which we learn what sin is.
Here is a much better commentary on the gist of Romans 7, specifically vs. 15-20 ...
By Charles Spurgeon
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Romans 7:15.
For what I would, that do I not; but what I hate, that do I.
This is a strange contradiction, — a man who has grace enough to will to do good, and yet does it not. There are two men in the one man, — the new nature struggling against the old nature. This must be a renewed man who talks in this fashion, or else he could not say that he hated sin; yet there must be a part of him still imperfect, or else he would not do that which he hates.
Romans 7:16.
If then I do that which I would not, I consent unto the law that it is good.
“If I do that against which my conscience rebels, so far, the better part of me owns the goodness of the law, though the baser part of me rebels against it.”
Romans 7:17.
Now then it is no more I that do it, but sin that dwelleth in me.
The renewed man still stands out against sin. His heart is not wishful to sin, but that old nature within him will sin even to the end.
Romans 7:18-19.
For I know that in me (that is, in my flesh,) dwelleth no good thing: for to will is present with me; but how to perform that which is good I find not. For the good that I would I do not: but the evil which I would not, that I do.
Oh, how often have men, who have been struggling after holiness, had to use these words of the apostle! The more holy they become, the more they realize that there is still a something better beyond them, after which they struggle, but to which they cannot yet attain; so still they cry, “The good that we would we do not: but the evil which we would not, that we do.”
Romans 7:20.
Now if I do that I would not, it is no more I that do it, but sin that dwelleth in me.
The true man — the newborn man — is struggling after that which is right. The real “I “, the immortal “ego”, is still pressing forward, like a ship beating up against wind and tide, and striving to reach the harbor where it shall find perfect rest. Oh, what struggles, what contentions, what rightings, there are within the men and women in whom the grace of God is working mightily! Those who have but little grace can take things easily, and swim with the current; but where grace is mighty, sin will fight for the mastery, though it must yield ultimately, for there can never be any true peace until it is subdued.]
Spurgeon