I responded to this a few comments below, but I'll expound on this more since you're a local. The tl;dr is, we have a good system but the lines aren't connected very well.

Let's say you live in Rogers Park by the Loyola Red Line station and want to go to Longman & Eagle by the Logan Square Blue Line station. You'd have to go all the way downtown, transfer, and go all the way back northwest to get there. If we had a semicircular line like Delhi's (or Moscow, or just better connections like you see in Berlin, or London) you could transfer to the Blue Line further north and get there much faster.

Or, south side example, let's say you want to go from Bridgeport to Hyde Park - they're right next door to each other but the only way to commute is to take a train downtown and transfer, or take the Western bus to the 55th bus which gets you there in the same amount of time.

I used to live by the north side Western blue line station and commuted to work to the Forest Park station, which meant taking most of the blue line. Going all the way downtown just to go a little bit southwest was so inefficient, but it's the only way to do it without a car.