A prof of mine made an off the cuff remark about Byzantine focus on charity led to an economic decline.

Kind of an odd comment to make about one of the economic powerhouses of the Middle Ages. I'd think all those massive territorial contractions and anarchic civil wars would have had more to do with economic declines than almshouses.

The Byzantines did see philanthropy as an important virtue and charitable institutions were often tied to a religious community. Unlike the west, there were no monastic orders so each monastery would often be founded with a specialized constitution called a typikon. These could contain very explicit instructions on how many beds for a hospital for the poor, or how to provision an almshouse, etc.

There were problems with monasteries amassing a great deal of wealth, though. Once a monastery acquired property, it was inalienable so over time a monastery could accumulate more land and resources than they could possibly use themselves, encouraging economic activity. In the eleventh century, there was an ongoing struggle between the monks of Mt. Athos in modern Greece (still there today) and the imperial government because the monasteries there accumulated great economic power (they were very close to Thessaloniki). Despite many attempts to curb the monks' economic activities, it seems like the monks went right on trading and buying up land.

But laymen could also economically exploit monasteries through the system of charistikion. Higher ecclesiastical figures or the emperor could essentially grant a monastery to an individual or a family for three generations. The charistikarios would be in charge of the administrative matters but not interfere with the ecclesiastical business to the monks. However, if the charistikarios was too greedy, he could endanger the very operation of the monastery.

Sorry to veer off topic there, but I wanted to show that religious institutions weren't necessarily economic drags. So really it's more complex than your professor makes it.