it's one of the best shows I've ever seen, and I can't really explain why
The reason is that it is REAL.
You are watching real life, or as close as a fictional recreation can ever come to it. This is why it so moving and gripping. It is a slap in the face and a wakeup call about what the modern American city REALLY is - with no added Hollywood bull shite (except season 5).
The show was made by people who had lived it (cops, teachers, street kids, journalists etc). It is basically a documentary (and it is even shot like one - the documentary visual style is striking from even the first episode).
It is the GOAT and it aint even close. To call it a "cop show" or "crime show" is totally missing the point. It is US (the American city). To confront that reality in the mirror is very disturbing and can make one question everything one believes or "knows".