Industrialization is a pretty complicated process and here are a few reasons:
Absolute technological level, despite the fact that people love talking about the ancient steam engine the steam engine was not nearly as decisive in industrialization as often thought. Improvements and innovation in machinery during the late medieval era played a huge part in industrialization. The first textile weaving machines for instance were based off of the mechanical clock which was invented during the Middle Ages. People often have a mistaken view, perpetuated by the science vs religion debate, that the Medieval period was a dark age when in reality it was in many ways much more innovative than the Classical era.
The Commercial revolution: industrialization was not just based on technology, but on easily obtainable capital to fund starting industries and inventors. As well as a financial and trade system which can sustain demand for products produced by industries. The commercial revolution of the 13th-18th century produced an environment conductive to that.
Agricultural surplus: To industrialize, you need a critical mass of non-food producing workers in cities and cottage industries. Agricultural productivity is necessary to produce food to sustain this population. Several waves of Medieval agricultural revolution and the addition of agricultural land during colonialism fueled the production of surplus foodstuff for industrialization.
1-3 was simply not present during the classical era in the Mediterranean because it has not developed those critical components yet. Basically people have a tendency of assuming "well James Watt invented the steam engine, ergo industrial revolution" while in reality you can easily argue the Industrial revolution was the culmination of 2000 years of human development.