The bitter series of conflicts between Rome and Carthage, known as the Punic Wars, raged on for over a hundred years. The third and final stage of this epic clash of civilizations took place from 149-146 BC. In the fifty years since the second Punic War, Carthage had grown in wealth and military power. In turn, this acted as an encouragement to subject peoples in the Roman Empire to rise up and stage rebellions against their imperial overlords.
Under the circumstances, Rome felt that it had no choice but to act. So long as Carthage existed, it would act as a constant thorn in the Romans' side. The general feeling among the Roman political elite was that Carthage must be destroyed. So once again, Rome made a series of impossible demands which they knew full well that Carthage would make no attempt to meet. One of these was that Carthage should be dismantled in its entirety and rebuilt in a much less threatening strategic location further inland. When the Carthaginians refused to accede to these demands, Rome immediately declared war.
The Romans lay siege to Carthage for three years. During that time, the Carthaginians fought bravely, but ultimately had no chance against the might of the Roman army. Eventually, the Romans breached the city walls and set about the wholesale destruction of Carthage, but not before the entire population had been captured as slaves.
On balance, one would have to say that the Romans were not acting in self-defense. The Carthaginians were not traditionally a martial people and only had enough of an army for their own self-defense. Thus they didn't represent a serious threat to the Roman Empire. Looking ahead, however, it seemed to the Romans that the Carthaginians might one day grow in power and wealth to such an extent that they would eventually challenge Roman supremacy in North Africa and the Mediterranean. So from that standpoint, one could say that the Romans were justified in going to war with Carthage, even though strictly speaking they weren't acting in self-defense.