I'm with Catherine on this one, although I don't find the passage odd. It only becomes odd if one presumes from the outset that Macedonian and Greek are only accents on the same language, in which case none of what Alexander says makes sense.
To go through your points - Alexander hadn't been speaking Macedonian up to this point because there were (as Philotas stated) non-Macedonians in the room. It appears they would not have understood him if he spoke Macedonian. He had been speaking Greek up to this point and Macedonian upper classes understood the language, most likely because they were educated in Greek. The Lebanese elite for example are often educated in French and fluent in the language, but it does not make Arabic and French the same language.
Speaking of a 'Hellenic' language family - Hindi and English both belong to the Indo-European language family. But that doesn't really indicate a great degree of affiliation. Given the geographical proximity, it can't be too surprising that if two separate languages were spoken in the Balkans, they would link back in the language tree at some point.
My sympathies on your problems with the Irish and Australian accents. I have seen many a Colin Farrel interview on the TV channels in the US, Canada, Britain, Australia, New Zealand, Asia etc. (used to be a bit of a fangirl
). Not once did they have subtitles for the my favourite Dublin boy. Similarly, Hugh Jackman, that singing dancing Aussie, hosted the Oscars recently. It was beamed all around the world but I can't recall anybody complaining that they could not understand his Australian accent.
Yes, Manarin and Cantonese speakers don't understand each other at all. The differences are apparently at least as great as those between Italian and Spanish - a friend who speaks both languages and lives in China assures me of this. You can label Italian and Spanish two Latin or European dialects. But I think most people would class them as different languages. I don't feel that languages are strictly tied to political unity. For example, China and Hong Kong seem to get along well now but China and Taiwan are another matter. I think Athena's Owl's point is a most cogent one. The definition of language and dialect is often politically influenced.
So, without going into any modern day silly nationalist nonsense, I'm going to stick with my original take that the differences between Greek and Macedonian as they were spoken during Alexander III's time are not comparable to different English accents. It appears they were at least mutually unintelligible dialects if not different languages.
I think it was not just Alexander III, but many of the Argead kings previous to him who were wannabe Greeks. Argeads claimed to descend from figures in Greek mythology but then so did everybody from Molossians to Illyrians. What the common people thought of these royal pretensions is anybody's guess. I think it's telling that the Argead claim of ancestry is first recorded in the context of a highly politicized situation where the Maceonian King had just switched Macedonia's loyalty to Persia from the Greeks. It would have solidified Graeco-Macedonian alliance and allowed him to enter the Olympics. It's also notable that there were serious Greek objections to his participation but realpolitik prevailed. But somehow that status quo didn't seem to last (one exception from memory). There appears to be no record of Macedonians winning anything in the Greek Olympics after that well into Alexander III's reign. They even had their own Olympics. I think if the Greeks accepted Alexander's ancestors' wannabe attempts, they would have allowed Macedonians to play with them.
Do you think Alexander III was a bit of a wannabe Persian as well?