The answer to 'why is my shut-off valve leaking water' is that the shut-off valve is likely worn out or damaged, causing it to leak. This is a common issue with older shut-off valves, especially those made of brass or other metal that can corrode over time.
The main symptoms of a leaking shut-off valve include water dripping or seeping from the valve itself, or water pooling around the valve. This can be caused by a worn-out washer or seal inside the valve, or by the valve itself becoming damaged or worn down. In some cases, the entire valve may need to be replaced to stop the leak.