A common fallacy in arguments about the existence of God

Arguments for or against the existence of God seem to suffer from a common logical fallacy. It is important to remember that if A implies B then it does not follow that B implies A. It does follow that if B is not true then A cannot be true. But, if we disprove A we have not necessarily disproved B.
In different words, one must distinguish between the necessary and sufficient conditions for something to be true.
Let me illustrate with a concrete example.
All German Shepherds are dogs. But not all dogs are German shepherds.
If we establish an animal is not a German shepherd we have not established that it is not a dog.

How does this play out in current debates about the existence of God?

Richard Dawkins destroys the argument from design which claims to establish the existence of God. Hence, he and many of his followers claim that he has shown that God does not exist. But, let us check the logic.
If the argument from design is valid then it follows that God exists.
Equivalently, if God does not exist then the argument cannot be valid.
However, the converse does not follow, i.e. if the argument is not valid it does not follow that God does not exist. All we can conclude is that the argument is not valid. This does NOT preclude the existence of God.

Now, let us look at some Christian responses to Dawkins.
If Dawkins is correct then God does not exist. Hence, if God exists Dawkins cannot be correct. Many flaws in Dawkins arguments have been pointed out. However, this does NOT establish that God exists. It just establishes that Dawkins arguments are weak.