Sort of loath to dignify the KidsnotSuits thing with a response. However, it could sway some opinions - so here's a quick stab at a response:
While criticising the Council for not undertaking Traffic Impact and Economic Impact assessments, KidsnotSuits make bold claims that the scheme will create "...phenomenal congestion" and "...wreck 26 Roseburn businesses". There is no evidence to support these assertions. However, there is evidence that the creation of high quality cycle infrastructure is good for local business, as shown here:
http://www.citylab.com/cityfixer/2015/03/the-complete-business-case-for-converting-street-parking-into-bike-lanes/387595/
It is worth noting that the Council states that traffic modelling is currently "ongoing" - which seems reasonable given the final design of the scheme is yet to be approved.
The scheme will also make Roseburn Terrace and Wester Coates safer and more pleasant for pedestrians. Pedestrians will be able to cross the road in one go, which is both quicker and safer for people on foot than the current two-stage crossings.
The scheme also involves some pavement widening and continuous pavements across side streets. More space and safer crossings at side streets are of particular benefit to people with mobility problems and people pushing prams and buggies as they remove changes in pavement levels and give clear priority to pedestrians over turning vehicles.
The proposed alternative (National Cycle Network route 1) has singularly failed to encourage people to cycle from the west of the city, as it is convoluted, unable to cope with high numbers of bikes and involves dangerous junctions and cycling in close proximity to trams and over slippy tram lines.
It is worth remembering that traffic congestion, and associated air pollution, is caused by too many vehicles travelling at the same time on the same roads. The historic street layout in Edinburgh cannot be substantially changed, so any solution to congestion problems requires people to travel by other means. Improving the attractiveness of cycling, walking and public transport is key to people switching modes. This scheme will substantially improve the attractiveness of cycling in the city - hopefully encouraging the "suits" to cycle to work with their kids to school. It doesn't have to be one vs. the other - we will all benefit from this investment.