You are still not making sense. If A does not equal B there is clearly both a case, separately, where "it's not A" and also a case where "it's not B."[1] When you add "...but also B" to the case "where it's not A" what is that supposed to mean? Also B in addition to what? In assuming that either A or B are the only two available options, for the sake of your attempted demonstration, clearly it is either A or B and not both simultaneously. If it's not A then clearly it's B. If it's not B then clearly it's A. When it is not one of the two, it is clearly the other but not in addition to anything else, it is that proposition alone. So, again, it is meaningless when you mention the "case where it's not A, but also B..."
Is there a case where someone says "I believe there is(are) no god(s)" and not "I do not believe in god(s)"(not A but B)? Sure. Is there a case where someone says "I do not believe in god(s)" and not "I believe there is(are) no god(s)"(not B but A)? Absolutely.
You conclusion is a complete non sequitur and your premises are a mess themselves.
[1] You may have begun to go awry when you used "it's not A" to signify when it is B and vice versa. That lends more easily to confusion than to clarity.