Essentially, there is no choice regarding existence. Existence just is. Space also exists without choice. Does electricity exist without choice as well?
A switch is either on or off. When it is on the current has a path to flow through the switch and power a device, and the circuit is said to be closed. When it is off the path is broken, or the circuit is said to be open. Current can not flow because the switch opened the path for it to flow, or it “disconnected” the path for current to flow.
So current is either flowing to a device when the switch is on, or it isn’t when the switch is off.
The potential is still there, but current flow does not exist with the switch off.
So the binary choice is to either have current flow to a device with the switch on, or stop the current flow by turning the switch off.
Many switches are marked “0” for off, and “1” for on, which is the traditional 0 or 1 for binary.