I agree to the extent that both are communicating between people but I've never felt them to be the same. You could probably say much more about the differences but I think it boils down to purpose and context. I can't compare it to learning a spoken language because I only have a little experience of that. The broad and vague purpose of spoken language is more about what you are communicating. With people you're sharing information, experiences, feelings or simply social interaction . Only some of that is about instructing people what to do or how to do something. Code is only about relating precise and limited instructions on how to achieve some goal whether it's part of a large system or a single much more focussed task. What surprises me about the article - maybe even shocking - is Not using logic seems wrong to me but it definitely explains a lot about my own code 😄 It’s not the same as language, and it’s not the same as math and logic
Learning how to express meaning in a different language is seldom 1 to 1. Even interpunction isn't always the same. You catch yourself constructing sentences around not using something that doesn't exist in your native language same as I did here to remove articles (which aren't present in Slavic languages). It often leads to excess verbosity. English-natives, in my experience, never really internalise declensions or gendered nouns unless they experienced them in childhood or use language with such on a regular basis. Sometimes it feels like translating Fortran to Prolog. 'Not being the same' is not synonymous with 'not using'.
Your point about not using parts used in other languages because they're missing from your mother tongue/s becomes very clear when you try and teach. I think the most surprising is that it's almost impossible to produce phonemes you aren't exposed to by the age of 2 IIRC. Of course it takes longer to actually produce the sounds but you need exposure at a ridiculously young age to even have a chance. I wonder if there's a similar limit with the more abstract higher level parts of language.