For example some artists may not want to "limit" their thought process to just logical, to more freely connect with and express their emotions (by no means am I implying that programmers lack of emotional connections). But after being trained to program it may be quite difficult to think any other way but logically.
I want to live in a world where I can find and talk to somebody who has not learned to program, who does not have any idea how computers work, but is exceptional in some other completely unrelated field, to see how they think, what their opinions are (which could be very different from my own yet extremely interesting). A world where (nearly) everybody has learned to program means it won't be possible (or at least very difficult) for me to do that.
Getting everybody to program of course has its many benefits to society, but the "What Schools Don’t Teach" video and similar articles always seem to imply that there is absolutely no downside, which I personally believe may not be true.