Cyrax hates Johnny Cage's movies. A lot. According to a bit in the Konquest mode, Cyrax "felt especially robbed of his eight bucks when he went and saw Ninja Mime."
Also, the mere fact that Cyrax, an assassin for the Lin Kuei clan that is very traditional/ancient in its customs (the "Cyber Initiative" aside), just went to the movies one day to chill out and watch a Johnny Cage film. Even funnier if you picture him doing this after he became a cyborg.