As the title says. The reason for this is that you never want to move the whole curve (well, unless we add it as a shift+drag), or if you did, you already did in the beginning before adding keyframes, or you can drag the few segments independently.

Anyway, the reason I'm saying dragging a segment between two keyframes is this (frequent) use case:

1) have a blank curve
2) add 4 keyframes near the middle, like so:

*-------------------*--*---A---*--*-----------*

Now, if you drag down segment A, you will have its two keyframes move in unison and keep the line straight, thus creating a plateau, like this:

*-------------------*\           /*-----------*
                      \*---A---*/

This kind of manipulation is insanely useful for doing fast changes in soundtrack volume.