It turns out that we are recycling wrong.
The US Recycling System Is Garbage | Sierra Club
You're Recycling Wrong | Sierra Club
As a rule:
1. As far as plastic goes, for the most part, we only really recycle plastic #1 and #2 bottles. All other plastic should really go into the garbage. (I am definitely an offender here. I routinely toss anything plastic into the recycle bin.) Plastic forks, knives, and spoons don't get recycled and jam up the sorting machines.
2. Paper that gets contaminated from foods and other stuff in the bin can't be recycled.
3. Shredded paper doesn't get recycled.
4. Paper coffee cups usually can't be recycled because of a polyurethane coating.
5. Styrofoam cups can't be recycled.
We used to ship our recycling to China, who would sort out the good stuff and discard the useless stuff. Unfortunately, much of the discarded stuff ended up in the oceans due to a lack of environmental regulations in China.
As one of the linked articles says, reducing and reusing are the first lines of defense, and recycling is the last resort. We shouldn't really count on recycling taking care of all the plastic that we use in our daily lives.