It seems simply to be a figure of speech. A double-edged sword literally cuts both ways. One of the earliest attestations in the OED for "double-edged" comes from a 1687 poem by John Dryden, The Hind and the Panther:

Your Delphic sword, the Panther then replied,

Is double-edged, and cuts on either side.

Here the sense is very metaphorical: "Delphic Sword" refers to the Hind's prophetic capabilities, which (and this is just from skimming the preceding and following lines of a long work with a lot of contemporaneous political baggage, so I might be missing something) run the risk of backfiring politically because of the zealous simple-mindedness of the followers it garners.

It's a fairly intuitive image and probably didn't need any basis in the actual danger of two-edged blades to make sense. For what it's worth, double-edged swords aren't much more dangerous to skilled users, since one usually shouldn't be touching their own weapon except intentionally, with, for instance, an armored gauntlet. The main reason not to sharpen both edges is that a single-edged blade is stronger laterally, so single-edged designs are preferable for slashing weapons (only one side is meant to be used anyway) or cheaper weapons (the added utility of a second edge isn't worth the investment in higher-quality metal). Even many single-edged weapons would have a bit of "false edge" on the back side, near the tip, to make thrusting more effective.