And yet you had to accept logic as valid in order to reach your own conclusion
This is how contradictions are found. You assume (not accept, but assume) something as true to see if it is consistent with itself or known facts. Now again, I dont reject logic. Thats your strawman of my case. I merely recognize that logic cannot work on its own. Your case is that logic can work on its own. But that means you have to use circular logic to prove logic, which is a logical fallacy. Thats the whole problem of your case. You cannot prove logic without using logic itself. The whole existence of logic in your case is completely unproved. Logical laws, such as "A=A" here, cannot in any way be proved. And that is the crucial problem here.
"A = A" is the logical law which must be true if logic is to be true. But it cannot be proved true in any way using logic itself, because whole logic depends on it and cannot be used to prove it at the same time.
So again, the problem cannot be solved. Law of identity itself cannot be proved to be true. So when you enter a debate here saying "Law of identity is true", it is not possible to prove that claim, because the proof already depends on that claim to be true and uses it itself. Its same as saying "truth exists". That claim is not possible to prove without using truth. And "truth proves that truth exists" is about as valid as saying "God proves that God exists" claim.
So again, in your case, law of identity proves that law of identity exists.
Thats a logical fallacy within logic itself. Logic is wrong according to its own laws when applied, hence contradiction.
If we say "A = A", then another law follows directly: "Claims can either be true or not true".
This is true tautology per law of identity, because "truth = truth", and thus "not truth =/= truth". We cannot say that "truth = not truth", because not truth is different from truth and then truth wouldnt be truth (truth =/= truth) and law of identity wouldnt be followed.
So these claims follow:
1. Claim must be true or not true.
2. "Law of identity exists" is a claim
3. "Law of identity exists" can only be true or not true.
4. To prove claim true would require proof which exists independently of the claim.
5. Things independent of Law of identity would be non-logic by definition.
6. Thus, only non-logic can prove logic.