Question

Why was Rome navy terrible in the first Punic War?

Answer 1

I wouldn't say Rome's navy was "terrible" at the time of the first Punic War, but Rome had needed to do much catching up in order to compete with the Carthaginian navy.  The Romans in Italy were originally a land-based, agrarian society.  When they did put together a navy, it was mostly for combating piracy, not naval warfare. 

Because of the threat posed by Carthage, Rome spent a decade or two building up its naval fleet, and in the First Punic War were able to score victories at sea over the famed Carthage navy - for instance, at the Battle of Mylae (260 BC) and the Battle of Cape Ecnomus (256 BC).