Why would he attack Arabia instead of Carthage or Rome?
That's a fair question. Of the three possibilities of Carthage, Arabia, and Rome, Rome was almost certainly never an option. The peninsular holds nothing particularly interesting at this point, as the Romans are not yet totally dominant, they haven't come into conflict with Magna Graecia yet, and they have no famous achievements to particularly speak of. You have to remember that Alexander was something of a glory hound, and Italy has none of that sparkle for him.
Now, of the two remaining options, Carthage was a likely opportunity. It was the traditional enemy of Greece, and Alexander put a lot of stock in panhellenic ideology. At least, to begin with. I'm of the school of thought that says that whole line of thinking was mostly for propoganda purposes and not really the way he thought. So for my mind that's a reason against Alexander choosing Carthage. Additionally, the Testament that stated an objective of conquering Carthage is of very dubious connection to Alexander himself, so that is not a good piece of evidence to consider. But in Carthage's favour, it controls some of the most productive grain regions in the entire Mediterranean at this point and is hugely rich.
Arabia may seem an odd choice, but there are at least some sources indicating that it was a place he had plans to conquer. Additionally, the region was more fertile around modern Yemen than in modern times, especially due to the native Arabic irrigation that had been developed including the ancient Ma'rib dam. Also, control of Arabia meant controlling all trade between the Mediterranean and India, as Aden was on the route between the Red Sea ports of Egypt and India. Indeed, in OTL this is why Aden became such a wealthy city. Arabia was also the producer of many of the ancient world's rarest spices, especially Frankinsence.