I think we have to be reasonable about this on both sides these days. I mean the cycling thing. The roads are very dangerous for cyclists and often a bike means one less polluting car.
I agree that cycling is better for the environment than cars, particularly single-person cars, but that doesn't mean that cyclists should use pavements.
There are cycle lanes all over the country, but if there are areas without them they should be brought in. I would love to see a 'fast lane' for cars with three or more people in them, to cut down on single-driver ones. If that happened (and I believe there is such a system in Bristol) then cyclists could share the single-drive lane. This would be safer for them, as there would be no overtaking.
Pavements should, IMO, be for pedestrians, and if others (eg groups of runners, an occasional cyclist, or whatever) want to share them, they should make way for pedestrians by default. If they are not willing to do so, but are unable to cycle on the roads, they should leave their bikes at home.