Over the last 40 years or so, Ignatius has acquired a reputation as an academic all star. A certain amount of prestige attaches to the school, which makes it more attractive to students and parents. The more status a school has, the more selective it can be. Some schools lower standards to increase enrollment. Iggy did the opposite, a smart move but a counterintuitive one.
Iggy wasn't always this way. Back in the '60s and '70s, it was like any other Catholic high school in Chicago. Now, though, it has the luxury of being able to turn students away, and to charge $20k for tuition. Ultimately, though, it's the student, not the school. By which I mean that a good student will thrive almost anywhere.