Wasn’t “all of Greece” united under Alexander the Great?

The greco-persian wars happened in the early fifth century BCE, roughly 170-150 years before Alexander became ruler of Macedonia.

During these wars, the greek city states (mainly Athens, Korinth and Sparta as those were the most powerful) fought united against the persians out of necessity and formed the hellenic alliance just before the second war (that one with Xerxes and the Battle of Thermopylae), but again, out of necessitiy and not a sense of shared nationality or other modern ideas.
And after these wars, the greek poleis returned to happily bashing each other again.

Some 50 years after (still around 80 years before Alexander was even born), Sparta and Athens (and their allies/subordinates, so basically all of Greece again) warred each other once more in the Peloponnesian War, but persian king Dareios II supported the spartan war efforts (mostly with money).

I think the meme refers to this clusterfuck of unstable relations between greek city states, but it does not narrow down the time period enough and I’d highly doubt Athens ever actually saw Sparta as a friend, a rival at best during the most peaceful periods maybe.

No Alexander’s Empire never conquered all of Greece. They established a hegemony certainly, but nothing approaching unification. Hot and cold conflicts would continue between Macedon and various Greek city states during Alexander’s conquests all the way until the Roman’s came.

Just because you defeated a country’s army in battle and claimed victory … doesn’t mean that the inhabitants or their army automatically become your friends and countrymen. Sometimes at the end of those victories, the only thing holding everyone together is the threat of more violence. All through history, victory doesn’t always mean that everyone gets to ride off with cheering crowds and everyone lives happily ever after.