So these Arab states want to shut down Al-Jazeera? Presumably because it is a news agency that has a good handle on what is happening in the region and is not afraid to offer articles criticising the Saudi and Egyptian authorities. The fact that these four Arab states have been joined by Yemen and Libya hardly adds credibility to their cause.
The talk about Qatar supporting terrorism may have some truth to it, but I think that is just a smokescreen. What the Arabs can't stand is the fact that Qatar is forging closer ties with Iran and together they share the world's largest natural gas field. The old maxim about following the money still holds true.