A flat disk will flip onto its side if you throw it like a frisbee. This is largely due to the fact that the center of lift (where the air is resisting gravity pulling it down) is in front of the center, which makes level flight unstable.

Not mentioned in the paper, but a frisbee generates a significant amount of both lift and drag on the rear lip, which is considerably more stable (in keeping with the beer theme, darts have fins in the back for a similar reason; if the fins were in front they would tumble).

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Did a bit more digging and my above explanation of a frisbee stability is not necessarily true. A few sources I found seem to credit the rim as increasing the moment of inertia. Certainly flying rings (such as the aerobie) tend to have a much less pronouced rim, which is in keeping with this idea, though the aerobie does still need a tiny rim for aerodynamic stability.

Frisbees are light and flat and they fly great, intuitively we think that being light and flat is all it takes to make a Frisbee. It turns out balancing lift such that a Frisbee does not flip is also really important. Things that are not designed with such balance in mind generally make pretty miserable Frisbees.

(Most of) All the things that fly do it because of lift. Lift acts like piece of string that keeps up the flying object. The point where this string is attached to the object is called the center of lift. This study shows that the center of lift for a flat round object used as a frisbee is towards the front of the disk. This results in the frisbee flying at an angle instead of flat because lift is pulling its nose up. This results in the disk eventually back spinning, making it bad at flying (think of it as the lift as yanking the front of the disk and causing a tailspin).