While I can't speak from a brewing perspective at all, I can relate information I've learned from brewers and brewmasters I've interviewed.
They all, more or less, have stated that a person is better off learning how to perfect brewing skills at home or through helping out at a brewery. For example, gain skills apprenticing at a local brewery before even stepping foot into the business side of things. Aside from financials, there's a lot to learn on a micro, or even nano level, that can make or break the business.
Going to school for brewing science seems like an exorbitant cost that can easily be replaced (on a different level) for free by helping out at a real brewery. In addition, you'll likely make some great friends and connections at the same time. You can even do this during the summer while still in school. In the end though, brewing beer rarely makes money, at least from what I've learned.
Edit: In regards to the "turning a hobby into a career" thing, I can't say that I agree, as I turned my hobby into an amazing career. While it's unrelated to beer, I still thoroughly enjoy it, despite the ups and downs.