This is a great question. There are several reasons for the growth of Phoenician cities during the Early Iron age. Let me give you the three most important points.
First, the location of the Phoenician cities was important. These cities were situated on the coastline of the Mediterranean. So, there were at the epicenter of other civilizations and trade was possible. Moreover, through the use of the sea, they were able to travel quickly and others could reach them as well. This geographical point cannot be underestimated.
Second, they were a great maritime power. Arguably, they were the most advanced at sea. They had amazing engineering when it came to ship building; they had no peer. Moreover, this lasted for a thousand years. Even as late as the war between Rome and Carthage, Polybius, the Greek historian, speak of their superior ship building abilities.
Third, the Phoenicians, were advanced intellectually during the Iron age. For example, they introduced the alphabet to the Greek and Etruscans. The Etruscans would share this with the Romans. The ability to write creates for levels of organization, which are not possible in a preliterate society. This organization allows for further growth.