The answer to 'why is my shut-off valve burst pipe' is that a burst shut-off valve is often caused by a buildup of pressure or a sudden change in water flow. This can happen due to freezing temperatures, corrosion, or normal wear and tear over time. Symptoms include water leaking from the valve or the pipe connected to it, and possibly a drop in water pressure throughout your home.
To fix a burst shut-off valve, you'll need to turn off the main water supply to your home, then replace the damaged valve. This is a job best left to a professional plumber, as they have the tools and expertise to do it safely and properly. Attempting to DIY a valve replacement can be risky and lead to further damage if not done correctly.