Why does the hook on the end of the Stanley tape rule move?

The amount the hook moves on the end of a tape rule accounts for the exact thickness of that hook.

If you are doing an outside measurement, the hook would be placed on the outside of the item you are measuring. A space would be left before the edge of the tape rule blade where that hook once stood. This space would be accounted for in the exact measurement on the tape rule blade.

If you are doing an inside measurement, the hook would press up against the edge of the tape rule blade. The thickness of this hook is also accounted for in the exact measurement on the tape rule blade.