Because I said so, that's why. OK, just kidding.
Actually, doing a set of 800m repeats is good for a number of reasons.
One reason is that it trains you to run about as fast as you need to run in a cross-country race. One could argue that there are times that you might be running faster, but high schoolers are probably going to be able to ratchet up to that higher speed well enough (for sprinting at the end, etc.) without training for it.
Another reason is that 800m represents a good distance that you might want to speed up during a race. Let's say you're running a course that's about 2½ miles long. The first mile or so, you're getting started, settling into your race pace, etc. At some point during the second mile, you will either A) start inadvertently slowing down; or B) want to pass a bunch of other runners, so will need to speed up. Regardless of the reason, this is a good time in a race to turn up the effort. If you do so for about 800m, you will put yourself in an excellent position to run an overall good race - you will probably pass some people, which will give you confidence, and you will now be close enough to the end of the race that you will start to speed up toward the finish (like the horse smelling the barn on a ride).
Of course, there is the mental practice you get running 800s, too. You have to run pretty fast during each 800m repeat, and you have to do it while you're tired. However, they aren't that long, so you will know that the discomfort won't last forever, as it can seem when you're doing mile repeats or a longer tempo run. Because you'll do more of these than the longer distance repeats, you get more brain training than when you do fewer of the longer ones. Each time you are running one of these, you are learning how to accept the discomfort that comes with running fast for a prolonged period of time (longer than a 100m sprint, say). Then, when you get in a race, you will recognize the feeling you have as relatively familiar, and won't panic ("OMG, I need to slow down!!!").
Finally, again because you will do more of these than longer repeats, you get a chance to refine your pacing because you get more attempts. If you're only doing 2 or 3 1600s, it's hard to get a feel for the pace. But doing, say, 4 or 6 800s, you get a much better opportunity to compare: "That one felt slower, but was 2 seconds faster than the one before last."