Why, in ancient battles, did being encircled mean defeat?
The classic example of that is the Battle of Cannae, where 80,000 Roman infantry were surrounded by 40,000 Carthaginian infantry.
Every description of the battle that I've seen talks in detail about how the Romans came to be encircled, but gives a hand-waving argument for why that was bad for them.
Wikipedia and other sources say that the Romans turned around and fought in a circle (It's not like individual Roman soldiers were being attacked from their unprotected sides or back).
Another "disadvantage" that's cited is that they were packed too tight, and didn't have room to wield their weapons. Presumably, they are saying that the Romans interlocked their shields. But couldn't they rotate their shields to create the necessary gaps between them?
Ancient battles are often described as a shield wall pushing against another shield wall. Since the Roman wall had a higher density of soldiers, wouldn't that let them push better, giving them the ability to dictate the position of said wall, expanding the circle?
One potential advantage of the encircled army is that its communication lines are shorter.
Are there any examples of ancient battles where encirclement did not mean defeat, that is, the encircled side broke out and went on to win the battle?