First they weren't professional soldiers. They were farmers. Professional or not, being outflanked is terrifying. Second, the troops weren't identical. Hanniba

First they weren't professional soldiers. They were farmers. Professional or not, being outflanked is terrifying. Second, the troops weren't identical. Hannibal had very experienced mercenaries with all sorts of different weapons, and his cavalry was far better than the romans. Third, Varro thought he'd crush the center of Hannibal's line and force the Carthaginians to panic as they fall back into the river by stacking Roman forces far deeper than usual. That shortened their line and made it easier to outflank. And pushing back Hannibals center naturally pushed his forces into an enveloping crescent shape. Fourth, the Roman infantrymen didn't know what was going on. The wind was in their face, blowing dust. The Carthagian army made enormous noise as it attacked. The roman troops were thirsty and hungry, Varro had drawn up his troops early before they could eat or drink. Lastly what destroyed the Roman cohesion was the loss of their cavalary. The Numidian cavalry crushed them on one side and barbarian cavalry crushed them on the other. Then the carthagians could wheel and attack the roman infantry from the back and sides, while their cavalry cut off any retreat.