Well, a sharp primary schooler can too... Bah, my first CS teacher claims now that it's crucial to start in primary school if you care about getting anywhere in IOI.
I don't think it's crucial to start early. Rather, there's a correlation--the sort of person to become a really good programmer or really good at CS is also very likely the sort of person to start programming at an early age.
It's a rare, rare high schooler that can learn how to use computer science. Most CS grads don't.
And we wonder sometimes why our software is so cruddy.