Why not Google Fonts?

The short answer is that Google Fonts is a great resource, and you can probably get away with using it pretty much all the time if you want to. The basic reasoning for both goes something like this, though:

When you use a CDN, the font will be cached so it can be used with any other website using the same font. It also saves you some bandwidth, since you aren't hosting the font files.

When you use locally stored fonts, the main potential advantage is not having to worry about being dependent on another service - things can happen outside of your control, like the server going down, or the resource you're using being moved or removed entirely. However, with the popularity and reliability of a service like Google Fonts, for example, a lot of these concerns are less... concerning.

Either way, it's probably good to know how to use a local font, at least.

Because your site needs to be available in China (Google URLs are blocked there).

Or, more commonly, because your client wants to use the (proprietary) font that matches their brand guidelines or their designer's approved page designs.

That's it. From a technical/performance perspective, Google Fonts is the best decision, always. They do way more than just store fonts; they optimize the crap out of those requests, beyond what you'd ever want to do. And there is practically no way that Google will be unable to deliver fonts unless the entire internet goes down. Plus, unlike other webfont providers (Typekit, cloud.typography, etc.), there's no JavaScript or validation slowing down delivery. So if it's up to you, use Google Fonts.