The Leica M3 doesn’t have the quick-load feature of later M models, and uses a removable spool to load film. You first put the film leader under the take-up spool spring, then the take-up spool goes in the camera, alongside the film cartridge. When you remove the take-up spool from the camera, the film counter resets. This happens because thanks to the mechanism that is inside the shaft where the take-up spool is inserted. The pictures that follows show how to take this shaft apart. Note that there are several slightly different versions of the Leica M3, so yours might be slightly different than mine.
Remove the screw at the bottom of the shaft
Unscrew this part with a wide slotted screwdriver
Once you unscrew the bottom ring (on the right) you can remove the internal parts
This spring is what pushes the clip that holds the take-up spool in place
The clip that holds the take-up spool in place
If you look inside the shaft, you can see a screw, remove it
That screw might be tight and there might be thread-lock and dirt, so you might have to use a chuck or a pin-vise to hold the shaft on the other end
The screw removed
There is a small spring underneath the screw
You can see some bushings inside the shaft
Remove the “pointy” part. Yes, that is the technical term for it.
There is a brass and a plastic bushing in the shaft
More bushings
A plastic bushing
and a metal bushing
Remove the set-screw
Unscrew the last piece from it. The piece on the right is the one that advances the film counter, but only when the take-up spool is inserted.