When an emergency happens, why do pilots need to stay on the current ATC frequency?
This doesn't mean you won't change frequencies if you move into another controller's sector or there's another reason for a handoff, such as moving from Center to Approach or Approach to Tower; it's to say that if you're already talking to ATC at all (often optional for VFR), then you should report your emergency there rather than switching to 121.5.

121.5 is monitored at every ATC facility, so if you have an emergency and don't know the right frequency to use, you can always go there and someone will answer you--and presumably give you a better frequency as soon as they've figured out where you are. If you already know the right frequency, though, then it's better for everyone (including you) to use that instead.