If one flips the greek 2 euro coin, he/she can see a maiden carried off by a bull. She is Europa/Ευρώπη carried off by Zeus, (transformed into an animal, a trope when it comes to Zeus' erotic escapades). He brings her through the Aegean to Crete and there he unites with her and makes three children, the eldest one being Minoas who lends his name to the Minoic Civilazation. Which is closely linked to Mycenean Civilazation, which leads unto Classical Greece.

I took a more liberal approach to the question whether the Aegean islands are considered part of Europe because literally the myth of the abduction of Europe takes part there. Or at least Europeans perceive it as such, if one takes into account the multiple European artists of various descents, who have dealt with the myth in their work.

Greece is considered the cradle of European civilazation and it aegean islands have been not only closely linked to mainland Greece, but actually was its first civilazation, the Cycladic one.

So as far as the Aegean islands are concerned, they are european by geography, by being the first important european civilisations, by participating in greek history which de jure is European and being contemporaneous considered European.