The point is that parking is something which can be provided privately, and which should, in theory (I know that, especially in economics, this doesn't necessarily mean in practice), cost approximately the same. Bike lanes, on the other hand, cannot be provided privately.
Isn't there some sort of city council that decides this sort of thing, rather than a sole executive? Most public works projects don't go through a referendum from what I've seen, which would be impractically unwieldy.