Up, Up, and Away!

Is there a potential disadvantage that I'm missing in the following proposition:

Step One: Secure credit card that accrues frequent flyer miles for cardholder.

Step Two: Pay outlandish school tuition and fees on said credit card.

Step Three: Reap frequent flyer miles.

Step Four: Immediately pay off credit card with student loan money.


Because I kind of think I'm a genius?