Is it true that the law was established by God so that we would sin more? According to Romans 5:20.
Moreover the law entered [literally, “sneaked in”], that the offence might abound. But where sin abounded, grace did much more abound. (Romans 5:20)
First let me point out what this verse does not say. It does not say that law came in so that we each would sin more. Paul is not giving license to sin, because he says three verses later, “Shall we continue in sin that grace may abound? God forbid!” (Romans 6:1-2) It is not saying that God established law for the purpose of causing man to sin. “Let no man say when he is tempted, I am tempted of God: for God cannot be tempted with evil, neither tempteth he any man.” (James 1:13)
It is wrong to take this verse out of its context. That context includes chapters 5 through 8. Particularly, a passage in chapter 7 may explain this verse better.
What shall we say then? Is the law sin? God forbid. Nay, I had not known sin, but by the law: for I had not known lust, except the law had said, Thou shalt not covet. But sin, taking occasion by the commandment [literally “taking the commandment as a base of operations for attack”], wrought in me all manner of concupiscence. For without the law sin was dead. For I was alive without the law once: but when the commandment came, sin revived, and I died. And the commandment, which was ordained to life, I found to be unto death. For sin, taking occasion by the commandment, deceived me, and by it slew me. Wherefore the law is holy, and the commandment holy, and just, and good. Was then that which is good made death unto me? God forbid. But sin, that it might appear sin, working death in me by that which is good; that sin by the commandment might become exceeding sinful. (Romans 7:7-13)
Law is good. Paul says, though, that sin used law to become more sinful. This is what is meant in 5:20. Not that God increased sin, but that sin increased sin. But as much as sin increased, God increases grace even more. That is the positive message of the verse.