I hear that phrase a lot. War on cars. First off, it is not pedestrians and cyclists that injure and even kill drivers. That aside, infrastructure improvements aimed at improving non-motorized transit do not always negatively impact traffic flow. In fact, sometimes new designs to implement bike improvements actually help traffic flow. Take the new two-way protected bike lane on 2nd Ave. Yes, the number of through-traffic lanes is decreased from 3 to 2. But anyone who has ever drove in Downtown Seattle knows half the trouble is turning: with so many pedestrians and traffic congestion cars often cannot turn and cause traffic to pile up. The new layout reduces and in some cases eliminates this by introducing a separate turning lane combined with a turn-only signal. Now turning vehicles are removed from the regular flow of traffic and are ensured adequate time and space to turn. Having drove 2nd Ave since the redesign I can vouch for how effective this seemingly small addition can be.
Cycling infrastructure needs to be built and improved because we need safer streets. But we also need smarter, more efficient streets and new cycling infrastructure is designed to make the most of our roadways. For more, Citylab covers the traffic impacts of protected bike lanes in an excellent piece on the redevelopment of several streets in NYC. Thinning lanes and creating turning cut-outs actually improved travel time for motorists!