Okay, so there are several reasons I am absolutely against this logic.
The age group you're talking about (between ages nine and...what, fourteen?) are not mature by a long shot. As @Penguinball said, their brains are still developing, ESPECIALLY at that age. They're dealing with hormones. Educationally, they really haven't learned a whole heck of a lot.
They are minors. They cannot legally:
Join the army (I know that eighteen year olds in the U.S. can do this, and there's a big debate about the fact that eighteen year olds can serve in the army, whether by volunteering or by being drafted, but they cannot smoke, drink alcohol or gamble, but that's tiptoeing into politics and I am going to firmly push against this becoming a political discussion)
Make medical decisions for themselves
Probably some other things that I am not thinking of at the moment
There are probably a lot of school systems where the kids have to walk to school, because they don't have school buses and they don't want the students taking city buses. How do you think these students would get to college if they cannot yet drive and are not anywhere close to getting their licenses? Their parents likely have to work. Some of these kids may actually be in daycare still.
College is for higher education. Professors do not expect to be babysitting their students (granted, they end up doing that even when their students are in the 18-early twenties range because of the way their students behave, but that's more on the individual student and less on the students as a whole). They expect their students to be able to come to class (on time), listen to the lectures, do their work, and get their grades. They do not want to basically still be teaching the basics that should be taught in elementary/middle/high school.
Unless you are a student prodigy (which is rare) who also has the maturity to handle the amount of coursework a college student has to deal with...you have no business taking college classes. (Exception: there are some programs in high schools where high schools can take college classes for credit as part of their high school requirements. I am fine with this, because at this point they're probably 16-18 years old and they're still developing their brains but not to the same extent as anyone in the 9-14 year age range. I was in a class where we had a student who was in high school and taking classes for college credit. He was very mature for his age and got his shit done.)
Some college students are taking six classes a day while also juggling their homework, jobs, and any sports they play. There's no way a child in the age range you're talking about would be able to handle that kind of workload. Kids that age need to be allowed to just be kids. It's bad enough when they're staying up until 8-10 PM trying to get their homework done and then having to be up early to be able to catch the bus and spend 6-8 hours in school.
So...yeah. I definitely disagree.