I read a segment of Aristotle's "Metaphysics" recently. When Aristotle said it can't be both A and not-A, he was rejecting the Pre-socratics, especially Heraclitus (all is flux) and Paramenides (all is one). His justification seemed to be we cannot talk coherently or meaningfully about the world without A and not-A. He didn't refute the Pre-socratics at all. His objection seemed pragmatic or practical, not at all metaphysical.