Huh, maybe my electrician wired it up wrong in my office then. I’ve got two switches in the room but come to think of it they perform more like an AND gate than an XOR. In the living room there are two switches and those are definitely like an XOR.
The XOR light switch is a trick. And, even if you know it is possible, it is hard to figure it out without someone telling you. My uncle and cousin were doing their own electrical work and couldn’t figure it out.
I had seen the trick as a young kid and remembered it 30 years later: install the one of the switches backwards.
One switch takes in power and puts it on one of two wires running to the second switch. The second switch connects one of the two wires to the power wire going to the bulb.
If you don’t know the trick, you get an AND switch.