"Provably" how? Many people learn through a class and go on to speak a second language, so what's the proof?

Sure, eventually you just have to use it. But as an adult learner, you can get going a lot faster by using your knowledge of other languages, understanding of rules, and so on, before jumping in, and it's not always practical for people to just take off and spend months or years in a foreign country in the hopes they'll learn a language while they're there.

The grandparent's point is correct, although he didn't say anything about formalized education. You inserted that yourself.

You can't just "disagree". This is a matter which science (linguistics specifically) has lots of research on.

If you're just saying that they're not perfectly identical, then that's obvious, you've said nothing. What I'm replying to is your implication that they're vastly different. Science shows that they're not as vastly different as the education system assumes.