Your cycling fallacy is…
“Cycling facilities cost a lot of money and are a poor return on investment”
Good cycling infrastructure does cost money, but it is incorrect to say it is a large amount in the scope of overall transport spending, or that it is a poor return on investment. Cycling infrastructure has been shown to pay back to society more than it costs – a 2014 UK government report cited returns of between 2:1 and 35:1.
Other countries demonstrate returns of 10 times or higher, and London's transport authority reports ratios of 20:1 for cycling investment. Whilst many of the UK figures are for ‘general’ investment in cycling (i.e. including training, etc.) the higher cost of cycling infrastructure is still justified because of the additional numbers drawn to cycling by the provision of safe places to cycle.
The Netherlands spends €500m per year on cycling infrastructure, which generates €19bn in health benefits alone – a 38:1 return on investment.