Because that reasoning – that your own utility is maximized by selfishness – literally cannot be right. If it were right, then it would be the answer all rational beings would arrive at, and if all rational beings arrived at that answer, then none of them would cooperate and everyone would be worse off.

This is not at all true. The fact that if people acted as I do, there would be no stable equilibrium is largely immaterial, because my actions do not affect how others behave. Unless I value "acting in a way that can be universalized," the fact that I don't do so has no effect on my decision making.

If all I care about is the good grade, and I have no value for personal integrity and whatnot, then if I'm an egoist and only care about myself, I should cheat. Other people are not egoists, and I can take advantage of this. If I am not an egoist and value integrity, or am too risk-averse, I should not cheat. There aren't a lot of genuine egoists out there, so this isn't usually a problem. Most of the ones that do exist tend to be constrained by the risk of punishment in many cases.