When two creatures are grappling, that's it: they are grappling. It's not one grappling the other; both are in the state we call "grappling," regardless of who started it. Usually.
The reason the stirge's ability is called "Attach" is to distinguish it from "Grapple." This is a special case, where the stirge is considered to be grappling, but its target is not. Hence, you can sneak attack an attached stirge, because it is denied its DBtAC, but not its target.
Stirges are not difficult to kill; it's just difficult to make it through a stirge-fight without losing some blood.
The reason the stirge's ability is called "Attach" is to distinguish it from "Grapple." This is a special case, where the stirge is considered to be grappling, but its target is not. Hence, you can sneak attack an attached stirge, because it is denied its DBtAC, but not its target.
Stirges are not difficult to kill; it's just difficult to make it through a stirge-fight without losing some blood.