I mean, climate change is coal (C) we take out of reserves in the form of oil and gas (from times where climate was warmer) and then burn it with oxygen (O) to CO².
Yes, plastic is a problem with pollution. But no matter how much we recycle it or if it rots away over centuries, hurting animals and poisoning environments: the end result is still that it is processed oil (C) out of a hole, contributing to greenhouse effect.