What is meant by "the passive voice remains 'an important arrow in the rhetorical quiver'"?

Solution 1:

A quiver is an open-topped carrying case for holding arrows (point-down) so that the archer can remove them easily without getting pierced by them accidentally. A "rhetorical quiver" would be a metaphorical holder for various rhetorical strategies, which Constance Hale compares to arrows.

Her meaning in the quoted sentence is that passive voice can be useful for some (unenumerated) literary or rhetorical purposes, though many experts on style take a dim view of it.

The arrows-in-a-quiver metaphor is a bit odd, when you think about it, since (presumably) an archer would normally fill his or her quiver with virtually identical arrows appropriate for a particular day's activity--hunting birds, hunting deer, target practice, warfare, or whatever. But Ms. Hale is by no means alone in using that turn of phrase, and perhaps archers in the old days filled their quivers with arrows of many different kinds, not knowing what they might want to shoot them at.

In any event, a more recognizably apt metaphor for modern readers might be a golf bag filled with different golf clubs, each of them designed for a distinct purpose, and no two of them alike. Passive voice would be one such golf club.

Solution 2:

It’s just one device out of many. You might perhaps say an important tool in the toolbox, if you want to be more direct. Many other similar metaphors are possible.