Why won't my hose bib handle turn either way?
The acme thread that allows the valve to open and shut has either galled or seized due to mineral deposits. At this point, you need to remove and replace the whole valve.

Since we don't have a picture, it's difficult to give further advice, but if it's a standard frost free, the valve is actually 8-12 inches back inside a tube on a long, easily broken valve stem and it's not easily repaired once it seizes.