In this case the "people making up financial benefits" were consultants appointed by the government, and the "other people's money" would also have been the government's. The "pet project" was initiated by the government, in a rare moment of enthusiasm for big ticket cycling infrastructure spending. And the "health congestion and economic benefits" of cycling are felt by all of us, not just those brave enough to get on a bike. I split my commutes between driving and riding. Let's assume for a moment that you share some of my route to work. Every time I get on my bike, there is one less car in front of you, competing for the road space that you want to use. In my case, I am lucky enough to have a largely traffic free route to work, so you do not even have to suffer the momentary inconvenience of safely overtaking me. Let's assume that you and I both rely on the NHS to keep us healthy. Every time I get on my bike, there are measurable health benefits that mean I am less likely to need to use the scarce resources that the NHS has which you also want to use. Let's assume that you rely on the tax paid by the firm that I work for and the people that I employ to fund some of the public services that you use. There are measurable benefits in terms of better physical and mental health and reduced absenteeism where people ride reguarly.
There are sound reasons for questioning this proposal, but they are not the ones that you have mentioned.
