Why did he hate Carthage so much? It seem like after the 2nd Punic war Carthage had given up on militarism and was content to be an economic power. Why did Cato push so hard for the city to be destroyed?
Cato the Elder is a strange man in general.
He was a staunch conservative; opposing change and following the old ideals of what it meant to be a proper Roman, and held every office from quaestor to consul.
He hated both Greece and Carthage passionately, this quote is attributed to him -'if ever the Romans became infected with the literature of Greece they would lose their empire'
Bradley lays out a convincing case for Cato's hatred of Carthage (and Greece) stemming from his deeply conservative attitudes towards both cultures. His hatred of Carthage stemmed from his deep fear that it would once more rise as a power to rival, and perhaps destroy, Rome. This is why he pushed for its complete annihilation so furiously.
So to summarise, he pushed for the destruction of Carthage because he was not satisfied with it remaining only an economic power. He feared greatly its possible resurrection as an enemy of Rome capable of bringing about her downfall.
Sources: Pamela Bradley, 1990. Ancient Rome: Using Evidence Plutarch, Cato The Elder Roman-Empire.net
Edit: still getting used to formatting, sorry :)
I would question the premise regarding Carthage's militarism--certainly its empire had collapsed after the Second Punic War, but this empire was somewhat recent and specific to the Barcid family. But its commercial power was unchecked (it was able to pay off the indemnity relatively easily) and any thought that it was really pacified is belied by the military harbor, still visible today, that was built in the second century. And Carthage was, after all, very nearby--Cato's famous moment was when he showed a Libyan fig on the floor of the Senate, saying it had only been plucked three days earlier (Plutarch, Cato, 27). And in te war itself Carthage was no pushover, as the Romans cycled through three different generals before landing on Scipio Aemilianus, one of the most talented leaders in Roman history, to actually make headway.
Obviously I'm not justifying the Third Punic War, which was pretty blatantly aggressive on Rome's part, but within he power politics of the second century Cato was not wrong that Carthage was a threat to Roman power.
