Why did Rome and Carthage fight in the Punic Wars?
Many wars start because countries or empires expand until the bump up against one another. At that point, they each see the other as a threat. This is what happened with Rome and Carthage.
Rome and Carthage were the two Mediterranean “superpowers” of their day. They each expanded within their own region. But since they were so close together (and since the Carthaginians were a naval power) they eventually came in contact with one another. When that happened, each side felt the other could be a danger to it.
This conflict, then, did not come about because of ideology or religion or any other set of ideas. Instead, it was simply about power. The two sides each wanted more power and each saw the other as a danger to its status as a major power.
It has often been said that most wars are fought over money. Both Rome and Carthage were expanding aggressively in the Mediterranean area. The ruling classes in both Rome and Carthage wanted more land, more import-export trade, more slaves, more power, more influence. They were the ones who advocated for war. The Roman senator Cato the Elder (234-149 BC) was known for using the same phrase in all his speeches, either in or out of context. That phrase is most often quoted as Delenda est Carthago (Carthage must be destroyed). The same economic motive can be seen in the wars between Athens and Sparta (the Peloponnesian War) and no doubt in the Trojan War, which was supposed to be about the beautiful Helen.