How can both ends of a river open into the same body of water?

Re: the Chicago River. I understand that the flow of the river was changed to cause it to flow* away* from Lake Michigan. However, the mouth of the river is downtown where it meets Lake Michigan and the north branch empties (?) into the lake about 14 miles north. Does water flow in the north branch? It surely seems so. But why? From where? what the…?

The north branch doesn’t empty into the lake. Water flows from the lake into the north branch. The water flows out into the Des Plaines River and eventually makes its way to the Mississippi and out into the Gulf of Mexico.

This map may help explain it:

The North Branch arises in a couple of marshy areas north of the city, one of them what we today call the Skokie Lagoons. The North Shore Channel, with its inlet at Wilmette Locks, is a canal built in the 1920s to increase flow into the North Branch. It joins the natural North Branch near Foster and Kedzie.