Carthage could defeat Rome, but it would never conquer the empire Rome had. It'd be difficult for Carthage to win the first war, and it'd be impossible for them to win the third, but the second is littered with oppurtunities. (shameless advertisement: see timleline in sig!)
Rome had a lot of advantages throughout the wars, but it is by no means impossible for Carthage to have won either of the first two. Carthage lacked the mentality to conquer Europe like Rome did - they were a trade empire, not a nation built on the military, and they had a much more limited citizen base. It would take a massive change of culture for Carthage to become 'Rome' enough to do something of that sort.