It's also worth noting that some of the Roman commanders were simply bad, and Hannibal himself was not without flaws.
The best example of the former is Gaius Flaminius, who was defeated by Hannibal at Lake Trasimene. [0] Livy memorably describes Flaminius as "not sufficiently fearful of the authority of senate and laws, and even of the gods themselves." Hannibal took advantage of his rashness to lure Flaminius into an ambush in which he and his entire army were annihilated.
Furthermore you could argue--and may still do--that Hannibal didn't even completely win Cannae, because he failed to attack Rome after his victory. His commander of cavalry remarked at the time, "You, Hannibal, know how to gain a victory; you do not know how to use it." [1] I'm personally inclined to think Maharbal was correct, but that's the advantage of hindsight.
These accounts are both based on Livy, who didn't let facts to get in the way of a good story.
Coincidentally, the excellent podcast, Tides of History, is currently doing a miniseries on the Punic Wars, and just covered why Cannae didn't end the war.
The Romans were actually quite smart after Cannae; they had lost a bunch of pitched battles, so they decided to shadow Hannibal's army to make his foraging logistics much more complicated (and forcing him to stay close to Southern Italy where he could easily resupply). The logistics of attacking Rome were therefore challenging at best, and the Romans used this as a delaying tactic to score wins on other fronts (since they enjoyed an overall manpower advantage).
One of my favorite anecdotes my history teacher shared was of Hannibal marching to the undefended Rome, throwing a spear at the gates, and walking away under the logic that if Rome could just throw away that many soldiers at Cannae, just how many more did they leave back home to defend the city?
perhaps "defeated" is a confusing word. Both romans and carthaginian armies suffered defeats multiple times. But there wouldn't have been a third punic war if carthage had been thoroughly defeated in the second as it was in the third.
The best example of the former is Gaius Flaminius, who was defeated by Hannibal at Lake Trasimene. [0] Livy memorably describes Flaminius as "not sufficiently fearful of the authority of senate and laws, and even of the gods themselves." Hannibal took advantage of his rashness to lure Flaminius into an ambush in which he and his entire army were annihilated.
Furthermore you could argue--and may still do--that Hannibal didn't even completely win Cannae, because he failed to attack Rome after his victory. His commander of cavalry remarked at the time, "You, Hannibal, know how to gain a victory; you do not know how to use it." [1] I'm personally inclined to think Maharbal was correct, but that's the advantage of hindsight.
These accounts are both based on Livy, who didn't let facts to get in the way of a good story.
[0] https://en.wikipedia.org/wiki/Battle_of_Lake_Trasimene
[1] https://en.wikipedia.org/wiki/Battle_of_Cannae#Aftermath