There are two issues - those of cyclists' safety and impact on climate - I suspect that the carbon cost of all the work that has gone on to create cycle roads in town (including the traffic hold-ups etc. etc.) will require a huge amount of cycling replacing motorised transport to even reach neutrality.
A fair point - but in the overall scheme of urban quality-of-life, of the benefits resulting from more cycling & fewer cars on the road, carbon's not the most important piece of the puzzle IMO. If we're talking in pure carbon terms, going vegetarian / vegan, eschewing air travel & cutting back home energy consumption to the bare minimum might make as much difference. Certainly as a regular cyclist, occasional driver, annual long haul flyer & unreformed carnivore, my own co2 footprint isn't markedly different to a non-flying veggie who drives a few times a week.
Cycling (the process) may be more carbon friendly than motor powered transport - but do not think that cycles, cycle clothing and (very specifically) cycle specific infrastructure does not have a carbon cost.
Nor does that same infrastructure for general traffic. Assuming the vehicle lifespan is the same, how does a steel framed bicycle weighing 15kg stack up against a 1.5 ton Golf? Not that the former can do all the jobs of the latter - but surely that's an argument for shared-ownership ZipCar schemes and the like. Road wear, maintenance & surface renewal.. yes, those roads need to be maintained anyway for goods vehicles, but discretionary & local trips account for a fair bit of the wear.
Where this infrastructure causes motor vehicles to drive inefficiently, including lengthening driving or waiting times these are additional carbon costs which can be attributed to cycles.
Again, I'm not sure if that's true of discretionary journeys. When applied to essential traffic, your argument makes complete sense - but the same could be said (to a far greater degree, I might add) of discretionary or substitutable motor traffic delaying essential motor traffic.