Nuclear energy is non-renewable because the energy nuclear power produces cannot constantly be replenished. An energy source must have resources that can be replenished to be considered renewable.
Nuclear energy is created by mining and extracting uranium. This process is dangerous and causes serious health problems for the miners, including lung cancer and uranium poisoning.
The amount of recoverable uranium resources is as limited as oil and other fossil fuels. The Uranium Institute has estimated that the existing attainable resources could only meet the world's current and future demand for energy for 42 years, so it cannot be classified as a renewable energy source.