The analogy is piss poor though, for the reasons already stated and ignored.
... groups, however defined, operate under rules and within infrastructure that advantages one group over others by design.
Do you think that is always a bad thing? A city may wish to encourage one mode of transportation over another, and for good reason, so they set up a system that favours one over the other, to encourage people to switch modes of transportation. Same as when they designate carpool lanes, giving those carpooling an advantage (or "privilege" since you seem so keen on calling it that) over solo drivers, who sit in traffic as the carpoolers zip on by. Do you really find that on par with treating people differently based on race? Such things teach you about white privilege?
It is also a bad analogy because motorists and cyclists are operating entirely different machines, and have entirely different needs and abilities, based on the fact that they operate these machines, which is how you identify them as motorists and cyclists. There are core differences between cars and bicycles, and not so much between races. Fundamental justice demands that we treat people of different races the same and allow them equal access to the same infrastructure (instead of Jim Crow laws). It demands that we treat motorists and cyclists differently and have different infrastructure for them.