Styrofoam is everywhere (Coffee cups, food containers, and in product packaging, and the downsides are many:
It takes up to 500 years to biodegrade.
Fifty potentially hazardous chemical byproducts are released during it's manufacturing.
It’s made from Styrene, which is a probable carcinogen.
When Styrofoam is burned, it releases harmful chemicals into the air.
Because it’s lightweight, Styrofoam that is not disposed of properly may travel and wind up in waterways, where it may eventually be eaten by fish or other sea life and cause harm to those animals. It is recyclable on a large scale, but there is no money in it because for every $1000 you spend to recycle it, you only get about $200 back (It's mostly air, except for the bad stuff).
In the past, paper coffee cups were used, crumpled paper for packaging, and paper plates for picnics and camping. You could even take a reusable coffee cup to the coffee shop and ask to have it filled.
Though Styrofoam technically is recyclable, the vast majority of it winds up in landfills, or worse, polluting the seas. We really need to stop using it for so much. It's a huge waste problem.