During the COVID-19 pandemic, many quantitative approaches were employed to predict the course of disease spread. However, forecasting faces the challenge of inherently unpredictable spread dynamics, setting a limit to the accuracy of all models. Here, we analyze COVID-19 data from the USA to explain variation among jurisdictions in disease spread predictability (that is, the extent to which predictions are possible), using a combination of statistical and simulation models. We show that for half the counties and states the spread rate of COVID-19, r(t), was predictable at most 9 weeks and 8 weeks ahead, respectively, corresponding to at most 40% and 35% of an average cycle length of 23 weeks and 26 weeks. High predictability was associated with high cyclicity of r(t) and negatively associated with R values from the pandemic's onset. Our statistical evidence suggests the following explanation: jurisdictions with a severe initial outbreak, and where individuals and authorities took strong and sustained protective measures against COVID-19, successfully curbed subsequent waves of disease spread, but at the same time unintentionally decreased its predictability. Decreased predictability of disease spread should be viewed as a by-product of positive and sustained steps that people take to protect themselves and others.