For such a contrary preposition, contra has made its gregarious inclinations felt in the English lexicon (English vocabulary words form the largest lexicon in the world) notwithstanding its contrarian nature, sometimes with surprising word histories. For instance, from an etymological point of view, a "country" is a land "opposite" another, in contradistinction to the land it is up "against." A "counter" is not only a piece of furniture that one leans "against" or stands "opposite" another person, but one can also "counter" another by speaking "against" her by holding an "opposite" point of view, perhaps by pointedly contradicting, or "speaking against" him. An "encounter," etymologically simply a coming up "against" someone or something, with a "con" might make you feel like the world is "against" you. Perhaps the "con," who does not hold your best interests in mind but rather is going to do something "against" you, might offer you some "counterfeit" money, or money "made against" authentic currency, the "opposite" of the real McCoy; if you did not recognize his devious and countermining contraband, you might have a real contretemps on your hands--bank officials would not be pleased at such an exchange "against" the normal course or "time" of customary fiduciary activity.
Would timepieces set in a "counterclockwise" mode really give us more time, or would they simply cause a great deal of discombobulation and "controversy," as if our linear notion of reality moving forward had "turned against" us by moving to the left? To tell you the truth, I could use some backward moving time, if only for about an hour or two per day. For more English derivatives of contra, check out a great Greek and Latin roots site which will show you, incontrovertibly, their power and influence over English vocabulary, a veritable Word Empire. And you can also view this root in a Greek and Latin roots poster.