By the biginning of the 5th century BC, Carthage had become "the" commercial centre of the Mediterranean region, Carthage controled the entire north African coast from modern Morroco to the boarders of Egypt, its influence had also reached Sardinia, Malta and western Cisily, it was'nt until shortly after Rome consolidated her power on all of the Greeks and the Italian pininsula including the southern Greek city states, that she turned her attention to Sicily that was occupied by both Greeks and Carthaginians. Rome's first involvement in Sicily was at the invitation of Messina, Rome eccepted because the conflict sparked an opportunity to declare war on Carthage.
The Punic war extended over 100 years, finally after a long and costly war, Rome prevailed and won. The strange thing was that Carthage was pretty much done after the second Punic war, when Rome placed an unbearable conditions on the Carthaginians and destroyed their fleet, why did Rome go into a third war we ask? Rome knew that Carthage will always be a thorn in their side if they dont wipe it from the face of the earth, and that's what they did.
Clearly Rome's reason for war was not related to "casus belli", they did not fight a just war. The Punic war was inevitable, it had to happen because Carthage and Rome were like two giants, they both controled a vast area of the world, and Carthage was getting richer, strong and great in numbers, which formed a big threat to Rome's safety. Rome started the war against Carthage only for one reason, is to seize her existance forever and the proof on that was the unnecessary third war against the already defeated and broken Carthage. Cato who always supported the complete destruction of Carthage said:"the liberty of Rome would never be secure until Carthage was destroyed." ( Appians, Punic wars 67-73).
I believe that Rome had the intension to destroy Carthage from the biginning, the burning of the city was unprecedented, despite the Carthaginian's