Why should drivers have first place?

NYC is a city. It has 8 million people. There is no room for private cars.

Where is the moped lane? Why is there only one bike lane? Every avenue should have two full-sized bike lanes (the same size as car lanes), one for each direction. Then a bus lane, and no car lanes.

If that doesn't happen, you can't blame bikers for riding on sidewalks or the wrong way in a one-way bike lane. You can't expect someone on a bike to cross to a different avenue just because they want to go the other way. It's the city's fault for failing to provide proper infrastructure.