That's a great analogy and I think often missed by many people. Spelling and arithmetic seem obvious as limitations in more complex fields (where communication and mathematics are involved). No one would say: "I can spell 'journalist' so I should be the editor-in-chief of the Washington Post." or "I can add 2 and 2 so you should hire me as an electrical engineer." (certainly not once they've grown up a bit, at least)

You have to advance to grammar, geometry, algebra, and more to find success in those fields.

But with programming, many people seem to stop at the point where they can program, and don't realize how much more there is to it (or not until much later). Programming is just the spelling/arithmetic level. Being able to design systems, select between different data structures and algorithms, understanding what a state machine is and how to structure your program using that concept, etc. These are the algebra and calculus of the field.