This is my life right here. I've decided I'm just telling everyone I'm going to Harvard, and they say "really?" And I reply "nah, just kidding, I'm going to Oxford"
That's not how logic works. You just said: X is not in A. X is in B. Therefore, if X were in A, A would not go to B. This is not a valid syllogistic form. For example, here is an argument of the same structure: Guns are not allowed in school. Guns ar