Trash disposal is a major issue for NYC. The city collections millions of tons of trash and needs a way to dispose of it. It is not cheap to dispose of trash. Just because you put it in the garbage, doesnt mean it doesnt have to be dealt with.
There are no more landfills on Staten Island so the trash must be send to landfills in either Pennsyvlania or Virginia which is not cheap. Its alot cheaper for the city to try to recycle at least some of the trash in various ways , otherwise your taxes will have to go up to pay for it