I thought this topic would be a gimme, but that's your first argument? You can represent symbolic mathematics in a programming language, or abstract algebras!

What you mean is this - programming languages are mostly imperative - they talk about how to perform an operation - but human languages are mostly descriptive - they talk about the real world.

From long experience, the number one difference is that human languages are much much harder to learn than programming languages.

I speak six human languages. The amount of effort it takes to get to "village idiot" level in a human language is hundreds of hours - to become fluent, it's thousands if not tens of thousands of hours.

I've programmed in... dozens of programming languages? Over a hundred? If you know a few programming languages, you can literally start doing something useful in a new language in the first day.

A human language is simply orders of magnitude larger than a programming language.