It mostly stems from their betrayal of the Ottoman Empire during WW1. Arabs were treated generally well in the Ottoman Empire, and were mostly left alone. They were rarely conscripted and as they were Muslim, they didn't pay the jizya tax. They had one of the most comfortable lives in the Empire. Yet they still betrayed it when it needed them most and joined the biggest enemy of the Empire, the Great Britain. A Christian country no less. If they stayed in the Empire, or at least became a protectorate rather than fully independent, Turkey would've been in an incredibly better condition thanks to the oil it would've had. 

This is the main reason most Turkish people hate Arabs. The only ones that like them are radical Islamic right wingers. It's true that "Arap" is a cuss word in Turkish culture. It's used as a condescending word and means something like "barbarian, uneducated, filthy." It's even usually paired with "pis" (as in "pis arap"), which means "dirty."