I have a light controlled by two "three-way" switches. It has worked properly for many years. It started getting a little flaky. I noticed that one of the switches needed to be pushed up a little harder for it to work. I replaced that switch (I checked the continuity of the old switch, and it was flaky). I got some of the functionality back, but not all. Then I pulled the other switch and it was bad as well. I replaced it and still did not get total function back. So, I pulled both switches off, and with no wires connected in either box and with the power on, found power going to each of the switches. I am baffled at how this could ever have worked. Is there any explanation other than I have some sort of short in my wiring?
There are three systems for multiway switching, though one of them has been banned in the USA for a very long time.
The "conventional" system. Power is fed to the common of one switch, which switches it between two travellers. The second switch then switches which traveller is connected to the light.
The "California" or "Coast" system. All three terminals of the switches are linked together. Power is fed in on one non-common terminal, the light is connected to the other.
The "Carter" system. The switches are wired to switch between hot and neutral. If the light gets two hots or two neutrals it is off. If it gets one of each the light is on. This is a bad idea for multiple reasons and was apparently banned in the USA about a hundred years ago but still you should be aware that it exists.
If you are finding hots at both switches I would suspect you most likely have the "Coast" system, though there is a remote possibility of the Carter system.