The Cause

Disposable cups are bad for the environment--and many are bad for human health.

According to Global Green USA:
Each year, 58 billion paper cups are used in the US at restaurants, events, and homes. If all paper cups in the U.S. were recycled, 645,000 tons of waste would be diverted from landfills each year, reducing greenhouse gas emissions by 2.5 million mtCO2e, equivalent to removing 450,000 passenger cars from the road. 
Many coffee cups are still made out of styrofoam, or polystyrene. According to GreenBiz:
Last June, styrene was listed as a possible carcinogen by the National Institutes of Health's National Toxicology Program. Several epidemiologic studies suggest an association between occupational styrene exposure and an increased risk of leukemia and lymphoma. 
Polystyrene is not widely recycled. The Environmental Protection Agency's annual report on solid waste recycling lists polystyrene cup recycling as "negligible." Foam particles are among the most common items found by environmental groups leading beach cleanups. Foam cups and containers break into small pieces that are easily blown in all directions by the wind. 
Carried through storm drains to the ocean, foam containers break down into small indigestible pellets which animals perceive as food, resulting in the death of birds and fish. Due to such concerns, more than 50 cities in California and 100 cities in the U.S. have banned or restricted the use of polystyrene food packaging.