Everyone understands things in their own way. The following is a very visual way to understand how a chiralkine system works. It uses ordered pairs of black and white cats in black and white rooms.
Here is an ordered pair of a black cat in a black room and a white cat in a white room.
The black cat in the black room is invisible. The white cat in the white room is invisible. The system can be visualized in terms of exchange of cats, rooms and combined cat-and-rooms, such that the cats appear and disappear through cycles of exchange.