Your cycling fallacy is…
“When cycling, you breathe in more air pollution”
This claim does make sense on a superficial level – cycling, even gently for transport, increases your heart rate and your breathing, therefore cycling will cause people to breathe in more of the airborne pollution produced by motor vehicles.
But many studies have shown that the air quality is worse inside motor vehicles. Harmful polluted air builds inside motor vehicles, which means that the people sat inside them breathe more polluted air than people outside them.