according to this article from Surfrider Foundation
Plastics degrade at an incredibly slow rate in landfills, but even slower in the ocean so the accumulation is greater. Here is a conservative explanation by NOAA.
A big topic of conversation these days is the "garbage patch" in the mid-Pacific gyre.
Again, here is a link to NOAA for a less reactionary explanation.
NOAA is a government organization staffed by scientists, thus tend to not make hyperbolic statements.
Whether you think that giant piles of plastic garbage are rapidly killing off marine life, which in turn is having a negative impact on the food chain to which we are directly linked, or if you think that a little garbage is floating in the ocean, doesn't it make sense to pay attention to how many plastic bags you are using?
I am constantly amazed that the default mode for cashiers is to put everything in a bag. If I carry two small items from the shelf to the cash register, then why do they need to go in a bag? It's a waste.