The law of small numbers is one of many examples of a phenomenon I call a probabilistic illusion
Just like optical illusions confuse the eye, so probabilistic illusions confuse our reasoning.
As we make more use of data this problem is likely be ever more prevalent, since so many people suffer from probabilistic illiteracy. Indeed even scientists and mathematicians get fooled frequently by these illusions.
Kahneman gives many examples of how our intuitive reasoning can jump to erroneous conclusions. I strongly recommend this book to help understand how this happens.