It's not their parking, it's street parking on public land. If the public decides through a council that the safety of the citizens is more valuable then a couple peoples parking spaces they can choose to reallocate that land. These people still have private driveways and garages to park there car whereas bike lanes can only go in certain places.
The city planners who made the decision to make the neighborhood car dependent are long dead or retired. These council members are trying to make it less car dependent and you want to bulldoze there houses for trying?
If we want to move away from car dependence we'll never get anywhere if we have to stop and consider every minor inconvenience that motorists may suffer and conive someway to put that cost on the people trying to change things.