HTML literally has language in the name, and C++ is a programming language.
Similarly, it's true that some humans can, with lots of cognitive effort, produce HTML and C++, but some can't. Even the ones that can don't do it the same way that they produce English or French.
This is the crux of the issue. GPT-3 would happily learn birdsong instead of human language, just like it has learned to produce snippets of code or a sequence of chess moves or various other things found in its training data. For that reason, it's not by itself useful as a model of human cognition. Which is not to say it isn't interesting, or that studying LLMs won't lead to interesting insights into the human mind--I suspect it will!