I think your argument is flawed. Programmers do think differently. It is similar to the difference between a shy introverted person with few friends and an outgoing extroverted person with many friends. A great salesman could take the introvert and get them used to more social interaction. The introvert could learn about all kinds of social cues and ways to connect with people in any situation. So then you say that there is no difference between an introvert and an extrovert - look at how many friends the introvert has now!

There are many people in this world that don't use analysis and logic in the same way that programmers do. That doesn't mean they can't learn, but the fact remains that many non-programmers currently do not think the same way.

I do think most people are capable of programming, but I think it is misleading to say that "programmer thinking" is something everyone already does.