Starting seeds in disposable thermoplastic cups has advantages; as a way to get an additional use from something that otherwise would likely be thrown away, because they are cheap, and they are a reasonable size for seedlings.
“Five gallon” buckets are another common plastic item that can be found inexpensively and used as planting containers. There are also a wide variety of other thermoplastic items that can be found and used (or reused) in a variety of ways by a creative gardener.
However, the thermoplastic commonly used for such items tends to be brittle, and prone to cracking under force, which can be problematic when making drainage holes in such items. Using a cutting blade can lead to splitting and cracking, damaging the container.
Thermoplastics are designed to be manipulated under heat, and unlike thermosetting plastics they can be exposed to heat and manipulated more than once. Using this property of the plastic, it is possible to make drainage holes quickly, easily, and without splitting using the heat from a soldering iron.
Even a cheap soldering iron will reach temperatures in excess of what is needed to heat plastic. In a well ventilated area, turn on the soldering iron and allow it to heat up. Then with only a light pressure, press the tip of the iron at the desired location, and it will melt a drain hole through the plastic. Do not leave the iron in contact with the plastic any longer than necessary, and take care as both the tip of the iron and any recently melted plastic with be hot enough to be a burn danger.
If done correctly, it will make a nice neat hole. For plastic cups I recommend a few around near the bottom edge, and one in the center of the bottom proper.
For anyone that commonly uses thermoplastic cups and similar as part of their gardening container selections, an inexpensive soldering iron can be a welcome addition and an improved method over trying to punch holes and risking splitting.