Your cycling fallacy is…
“When cycling facilities are built, people often don’t use them, but cycle on the road anyway”
This can often be true – many cycling facilities around the world are of a poor standard, failing to enable safe, simple, uncomplicated journeys. People who choose to cycle anyway will typically avoid poor-quality cycling infrastructure, because their journey would otherwise be slower and more difficult than just riding on the road.
In fact this is an argument for creating high quality cycling infrastructure which people will chooseto use: well-designed facilities typically see significant uptake – for example in the UK, the new cycleways in London, or the Bristol-Bath cycleway.