Meow, why couldn't God have created logic? There is no reason why A = -A couldn't have been possible before God said "Hey, cut that out. You're not allowed to do that anymore."
You're argument fails because you assume your conclusion: Namely, that logic always existed, and therefore takes precedence over God.
You've contradicted yourself in your hypothetical.
Who do you suppose could have said "hey, cut that out?"
God?
God = God? Necessarily so.
See the contradiction?
Identity is incorrigible, which in epistemology means that even attempting to negate it must assume its truth. No matter how you word it, no matter what you do, any attempt to deny the ontological necessity of identity will self-refute.
"It's possible that identity is false." It's possible that what is false? Identity. (Identity = identity)
"It's possible God created identity." It's possible what created identity? God. (God = God)
Any such attempt puts the cart before the horse. It is not rationally possible to doubt identity or to suppose it's contingent on anything; that is an absolute fact. By absolute I'm not just putting a strong emphasis on it being "most likely true, times a google zillion billion" or anything like that. By "absolutely true" I mean that the statement "Identity may be false or contingent" is infinitely justified to be false.
This is one of the rare examples of a knowledge that humans can know absolutely, without even the remotest possibility of the knowledge being wrong. This is an absolute knowledge humans can possess; that identity is efficacious and ontologically necessarily existent. Any human who attempts to disagree, no matter how cleverly, ultimately self-refutes.