Why do many people reject science in favor of mysticism, anecdotes and instinct?

There are many examples of our collective failings as a society to understand and incorporate math and science. Many people bet the lottery, or gamble at casinos, despite overwhelming evidence that the odds are stacked against the individual.

Likewise, there are many people that hold on to outlandish notions (vaccines cause autism, homeopathy, etc.) or reject clearly done science (evolution is false). Where does this arise? Is this a failure of education in math, science, statistics and probability? Have scientists failed to present data clearly? Are we inherently visceral creatures? Is there any way to correct this through education or outreach, or are we “doomed”?