Start with a hand-wavy definition of consciousness. Move the goal post whenever your stated prerequisite of consciousness is reached and resort to unfalsifiable assertions about qualia.
And throw in some category errors while on it: when you're talking to Claude, you're not actually calling a stateless LLM directly, you're talking to an AI system (and yes, that's often just three LLMs in a trench coat). But claims about the topology and workings of a single LLM are as relevant to the question of consciousness as claiming that humans can't be conscious because the limbic system doesn't technically support it.
Coincidentally, I just attended a fantastic conference on machine consciousness (https://machine-consciousness.ai). It's a fantastic place where literally all speakers disagreed with each other, and yet found an incredible amount of common ground.