I think most of the boundaries of todays continents developed not as much as strictly geographical divisions but more along geopolitical and ethnographic lines. The fact that most often they use coastlines as division lines is just a geopolitical feature.
So if for a thought experiment, an alien geographer who had no notion about our concept of continents, would be tasked with writing a geography of Earth, he would quickly establish there is a Chino-Asian, Indo-Asian 'European-western', South-American, middle-Eastern, and Southern-African block of regions, a distinct island-culture in the Pacific And a large uninhabited, frozen landmass at the South Pole. (If he doesn't consider land-masses that important, he might also add the islands and ice-masses of the arctic as an additional entity)
Refining his 'region groupig', he will quickly lump Japan with the Chino-Asian regions, and probably merge India and a few other countries with them for geographical reasons, calling them 'Continent X, eastern part and Continent-X western part. Likewise he will originally lump Europe, Australia and North America together for having the same culture and ethnography, but split off Australia for being too far away from the others and having a likewise but still distinctively different zoology. If this were the 1400's, he would move North-America with South-America into one group, by 1800, he would split the two, but keep North-America a separate region. Today, he would probably merge North-America and Europe together.
No idea what he would do with the 'near East' and 'Middle East': move it with Sub-Saharan Africa, move it with Europe and make the Sahara the boundary between the continents or keep it as a separate entity, possibly including Pakistan and several majority-muslim islands in Asia.... My guess is as good as yours
Still, his division will be between 55 and 75% compatible with our 'western' division of 'continents'.
To recap, our current notion of continents is a pretty arbitrary division stemming from notions of the Greco-Roman world, adapted to fit over the ages to fit our understanding of the world. Could it be done differently? Surr, done better? Probably. Would it matter in the end? Not really. So what gives? Why ask. It's still a nice topic to debate on sites like AH.com