So this guy is trying to argue that in the future everyone will have to be able to program? This seems illogical- yes, programs will need to be written, but won't it more probably be done by teams of experts, as it is today? Will everyone need to have homegrown software for a reason I don't understand?

Is he maybe arguing that everyone will have to be able to read every programming language in existence JUST IN CASE every user interface disappears off the face of the earth and every programming literate person in existence disintegrates?

Everyone needs to be literate in a human language because that is how humans communicate. Computers have built-in translators, because they are tools. Why on Earth would every professional be needed to write his own programs, and debug his own copy of Internet Explorer 200.5?