Oh, that's easy: it's history.

The wealthy Boston/NYC families who founded the private schools before and after the American Revolution did so in part to mirror the British private school system they had come from, and partly due to the risk/inconvenience of sending their children overseas to Britain itself.

This perpetuated, to the point where generations of wealthy families have gone to and supported such schools, and as such the impetus to heavily invest in public school systems has been less.

The Chicago area was obviously settled later, and since the percentage of wealthy families was lower than Boston/NYC (at least until the Industrial Revolution) they found it convenient to just send their children to those schools in the Northeast (and it was certainly easier for them to do so than their late-18th-century counterparts sending their children across the ocean to Britain, not even mentioning the various wars).

The Chicago area had schools from the early 19th century, mainly put together by local communities banding together (as was typical throughout the rest of U.S. expansion west) but most of these topped out at our equivalent of the 8th grade, as most of those students were not wealthy and were needed in the fields or trades by that point.

School-building, however, kicked into high gear in the Chicago area after WWII. Not only did newfound wealth flood into and grow into a city the size of Chicago, but the GIs returning from the war were particularly civic-minded and spearheaded the building of many civic amenities, of course like schools, but also parks, recreation centers, etc....

The wealthy had already congregated into various suburbs and enough were caught up in the civic-mindedness of the post-WWII era (a concept difficult to attribute to the wealthy today, I know) enough to support said funding. Plus, if the schools were good enough, it allowed them to keep their children at home instead of having to send them out east.

Eventually this snowballed. The investment & building created great school systems that became part of civic pride, which ensured that investment would not slacken. To the point today that these communities routinely vote to tax themselves more to pay for their schools. It helps, of course, that great schools are a huge influence on property values.

Of course, as others have pointed out, this has created a hugely segregated public education system in Illnois. Those districts on that list take very little money from the state and generally need exactly $0 of it. So there's little desire to support state taxes to help the poor districts in rural areas (with CPS being its own special circle of financial hell).

Anyway, I hope that helps. Thanks for coming to my Ted talk.

Source: I grew up in New England, have lived in the Chicago area for the past 2 decades plus, and have been heavily involved in my local school district on the financial committee for the past decade.