First, Arabic itself is an incredibly fragmented language. Almost every country or region that speaks it has its own colloquial version of it which may or may not be mutually intelligible. As a Lebanese person I can understand Syrians fairly easily, Jordanians with a bit of straining and the other person speaking slightly slower than usual, Egyptians with a lot of straining and speaking slowly and Saudis not at all. Theoretically, we could communicate using the formal(written) Arabic, but most people, especially newer generations, tend to suck at that as it's a much more difficult language that's learned only in the context of school and pretty much almost never used outside, at least in Lebanon, that is. The colloquial languages are to the formal Arabic as French/Spanish/Italian are to Latin, basically.
Second, all good universities I know of in the region teach in English or French rather than Arabic. Though the trend is tipping towards English of late. This is because most of the region was put either under British or French mandate after the Ottomans were ousted during WW1. This was detrimental in many ways which I won't go into, but one of the good things that came out of it was that they established many schools and universities. In fact, most of the good ones I know were founded by French, British or American missionaries during that period.
Third, well, the internet(and media in general), English is the dominant language in media most people consume. I learned English from watching cartoons as kid. I've almost never stepped foot in an English speaking country(except for a couple of weeks in the U.S. 2 years ago) and yet I can speak, and write, with almost native proficiency.