The three options that provide evidence against the author's perspective in "Three Cheers for the Nanny State" are:
A. Some people do not care much about their health. E. Some people can regulate how much soda they drink. F. Some people think that exercise is more important than diet.
These points argue against the idea that government intervention is necessary for improving public health, suggesting that individuals may have the ability to make health decisions or prioritize other aspects of their lifestyle.