I disagree, somewhat. I think one cannot become a skilled code-reader without knowing how to write code. One cannot be a skilled code-writer without knowing how to read code, and having read a lot of code, but without having written any code, I don't think reading code provides any enlightenment.
My small-steps progression would be writing Hello World, writing a smallish program, learning how to read code, writing code that you have to maintain, becoming skillful at reading code, becoming skillful at writing code.
I agree with you on natural language, that one must be a skilled reader before writing. I think the reason I see a difference between code and natural language is that the baby-steps of writing code can be mapped onto speaking natural language. I don't think one could become a skilled reader before being a proficient speaker in one's native tongue.