Religion says that we know evil exists for God the creator of all opposes it and works only and totally for good.

That is why it refers to evil as a problem for those who believe in an all good and all loving God. It says that if we say there is no God because evil exists then that makes no sense and we are left with no way of knowing what we mean by good.

So if you deny God over the problem of evil you end up with a new problem - the problem of good.

Then there are two problems. The problem of evil. The problem of good.

If there is a problem of good and logic is good then it follows that there is a problem of good logic. You could say that we need to explain good logic and God is the explanation. But to find God through logic you need to deny that logic necessarily proves God. You need to work out logically that logic can be trusted. You cannot say, "God gave me logic. Logic says God can be trusted. Therefore logic can be trusted." That is an illogical circular argument. It defies logic. You are bringing God in to cover up the fact that you are thinking for yourself without him. What does not defy logic is, "If God gave me logic then I have to decide for myself independently of him if it is correct. I then have to justify my belief in his existence with logic. If logic debunks him then so be it."

The failure of the problem of good logic to show that there must be a good God shows that there can't be a God!