"Frenemy" is actually in the Oxford Dictionary.  It was added in 2010 along with its friends "vuvuzela" and "chill pill".   (I just thought of a great high school English assignment - write a poem using "frenemy", "vuvuzela", and "chill pill".  But I digress.)

A "frenemy" is defined in the Oxford Dictionary as "a person with whom one is friendly despite a fundamental dislike or rivalry".  The use of "frenemies" dates all the way back to the 1950s. 
"Frenemy" has even landed its own Wikipedia page.

What did we call frenemies before, well, frenemies?  And more importantly, why do we even have a need for this word?

• Are we friendly with people we dislike because we feel socially obligated to do so?  (A work environment, for example, would be a situation where it may behoove you to be friendly to your archnemesis in the next cubicle.)

• Are we friendly with people we dislike because we find (to quote Star Trek) that resistance is futile? If you're going to be around Uncle Aloysius for every holiday, you may just zip your lip and be quiet for the sake of family harmony (I apologize to those of you with an adored Uncle Aloysius).

• Is it because we have difficulty stating our feelings and needs to someone who we just don't get along with or has treated us poorly?   (So we just continue to put up with it.) 

• Is it because our frenemies are more like us than we want to admit? (In the words of Bill Shakespeare, "familiarity breeds contempt"). By rejecting them, we may feel like we are rejecting ourselves.

• Is it because the good parts of the friendship outweigh the bad?  (I guess it depends on the severity of the transgressions.  If your frenemy threw you under a bus, metaphorically or literally, that may be something even the good stuff can't outweigh.)

• Or are we just gluttons for punishment?   Do we feel we deserve the frenemies' wrath in some way?

Why would we even want to continue contact with certain people when we are a target of their anger, or when we have a fundamental dislike of them?