What are the most subtle ways to deceive people with statistics?

Subtle... I like the ones that exploit exponential effects or the birthday paradox.

For example: Men are <10% taller than women on average. But if you look at a largish group, the probability that the tallest person is a man is ~99%. With a bit of writing skill, that probability can be used to make the difference seem like 20%, 40% or even more, whatever the writer wants.

Create a sampling bias. When you want to prove cats are more popular than dogs, survey people buying cat food. If you want to prove the opposite then survey people buying dog food. Quite a lot of the statistics you read in otherwise reputable news organisations will have sampling errors like this, sometimes intentionally.

Hmm, let me try.

An internet poll suggests that Rick Astley's "Never Gonna Give You Up" shall be the new US national anthem.

The sampling bias is that everyone who doesn't use a computer often probably never came across the poll

Limit historical data to fit your “conclusion”, pick the data set(s) that fit(s) your “conclusion” best and eliminate or highlight data points that are far-out.