You have the idea of noise cancellation backwards. This feature blocks sounds YOU may hear, not what others will hear from your microphone. Pease see Apple's description. It is copied from:
Active Noise Cancellation and Transparency modes for AirPods - Apple Support
What are Active Noise Cancellation and Transparency modes?
In Active Noise Cancellation mode, an outward-facing microphone or microphones detect external sounds, which your AirPods 4 (ANC), AirPods Pro 1, AirPods Pro 2, or AirPods Max then counter with anti-noise, canceling the external sounds before you hear them. An inward-facing microphone listens inside your ear for unwanted internal sounds, which your AirPods Pro or AirPods Max also counter with anti-noise.