The illusion framing/answer falls apart with some minor prodding.

What makes the computation in the brain special from other physical processes to give rise to this illusion?

The sewer system in NYC is complex. Does that also have the same illusion? Does the sewer in NYC have consciousness?

What makes brain computation special? Nothing. That's my whole point. Does the sewer system in NYC have consciousness? It's impossible to answer, because there's no single accepted definition of consciousness. If something isn't clearly defined, it becomes very hard to meaningfully assess whether it applies or not.

But if we built a Turing complete, sewer-like system that simulated every neuron in a human brain, it will claim that it is real and conscious for sure. There's no paradox at physical level, intuitively conceptualizing it is the "hard" part.