There are more cyclists on the road every day, and whenever anything is proposed to accommodate them, encourage them or keep them from getting squished, there is pushback from the status quo. In New York, a bike lane just got delayed because " repurposing space from cars to bikes would impede emergency access, endanger seniors, and destroy “the historic nature of the Avenue.”
Every one of these complaints is false or can be addressed. That's why this page from the Cycling Embassy of Great Britain is so useful; they take each of the fallacies and provide a response. Questions like:
Also on every answer page, they provide links and resources to background information, statistics and more to give you even better arguments.
I should mention that just because you give people this answer, it doesn't mean that they are going to listen. There is a Facebook page I follow that promotes walkability, but seems to have devolved into a rant site to attack cyclists who ride on the sidewalk, making it sound like the biggest problem in the City. I do not deny that it is a problem, but thought there should be some perspective and balance here.
I used all the same responses that the Cycling Embassy does, describing the ride on Dufferin Street, shown above, where the cars are all driving at 60 MPH and the sidewalk is empty and I was too terrified to ride on the road. I suggested also that safe cycling infrastructure was the appropriate response, and that there was not much danger to pedestrians here since there were none. The response I got- "that old 'cars do this and that' argument has no cred re the subject of sidewalk cyclists. There is zero justification for riding your bike on the sidewalk" was not sympathetic.
The same can be said for many of the other responses myths and fallacies; (look at “Cyclists ignore red lights” as an example) You can give these well reasoned arguments until you are red in the face but facts are one thing, opinions and anecdata are another.