Why not use steel or fiberglass for flywheels instead of carbon fiber

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Facial
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It's come upon my interest that besides capacitors, flywheels can also be used to store considerable amounts of energy at impressive levels.

The best material is supposedly carbon fiber, since it can spin at high speeds.

But what about other materials like steel fibers or fiberglass? Those materials can be pretty strong too. So I was wondering why those materials aren't used for more economically suitable applications.
 
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I can't find it right now, but there's a fairly recent (past month or so) thread about that around here somewhere. It goes into a good bit of detail about the properties of various materials for this application.