Plastic items can take up to 1,000 years to decompose. A plastic cup will take on a very conservative estimate at least 50 years to decompose. At the same time, over 16 billion disposable coffee cups are thrown away each year. These are coated in plastic and would amount to a bare minimum of 800 billion disposable cups lying in landfills at any moment (assuming the values stay the same). These plastic cups not only waste space, but can also release harmful chemicals into the soil during decomposition, ruining the area they were disposed at.
Buying 100 disposable cups can cost even less than $7 which explains the tendency to use them. Due the cheap cost, most consumers would turn a blind to the environmental consequences that the future generations need to deal with. Although the production of one disposable plastic cup is much more eco friendly than a reusable one however it is a one use thing. A reusable variant is actually more cost efficient than their disposable counterparts beginning from less than 10 uses for plastic coated cups and around 50 for styrofoam.
Paper cups are a great alternative to plastic ones as they are biodegradable (capable of being rapidly decomposed whilst avoiding pollution). However it is possible to recycle both types of cups and it would save the energy needed to procure the materials neccessary to produce more cups. But sadly this would only work in the most optimistic of scenarios as there are too many citizens who either don't have direct access to recycling options, or are too lazy to be bothered.