Your cycling fallacy is…
“Converting road space into cycleways slows down motor traffic which makes air pollution worse”
The idea behind this fallacy is that taking road space away from motor vehicles will increase congestion, resulting in more motor traffic jams, thus increasing amount of pollution they generate.
But where roads are already busy, pollution levels will already be high, and in the examples of cycling infrastructure taking road space from cars there has been minimal difference in the levels of congestion and pollution.
The argument follows reasonable ‘common sense’ principles, but it naïvely presumes that removing road space has no effect on peoples’ choice of transport mode – adding more space for motoring has been shown to induce demand (i.e. encourage more people to drive) while creating safe environment for cycling has been shown to enable people to switch to cycling for journeys which otherwise would be driven.