Is it true that "not everyone can be a programmer"?

Found on Ars Technica on Sunday, 16 September 2012
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An old adage that many programmers stick to: "It takes a certain type of mind to learn programming, and not everyone can do it."

People may study success in college-level courses and conclude "some people aren't fit to learn programming". However, such a conclusion severely oversteps the bounds of the observed evidence. How much failure could instead be attributed to how the programming is taught (too abstract?), or which style of programming is taught (too imperative?), or the programming environment (compilation, no immediate feedback?).

Of course you can blame a lack of education, but that does not change the fact that some people are not able to be programmers. There is a certain way of breaking up a problem into logical pieces in your mind, and that's not something everybody can do. The majority maybe, but not everybody.