I mean the simple answer is to break the monopoly that china had. But why? What interest would monks have in it? Or was it a part of a plot from the Church so that the Church could gain more revenue from silk based products and to steam the tide of money going east.
I mean i sounds more like something from a comedy movie. A group of people posing as monks to smuggle worms out of a country. Are we even sure they were real monks?
The source of the history of the monks smuggling the silk worms out of China is Procopius (an Early Byzantine historian).
http://traumwerk.stanford.edu/philolog/2011/08/byzantine_silk_smuggling_and_e.html
According to him, the monks were operating on behalf of the Emperor Justinian.
First monks were sent to India (as spies) to investigate ways to import silk more cheaply into Constantinople. The silk trade had been going on for a long time. But control of most of it had become monopolized by the Persians, who seem to have been driving up the price. The Eastern Roman Empire was aware that silk could be purchased in India, and transported across the Indian Ocean to Egypt and thence to Constantinople. The monks were sent to investigate this route.
The monks returned, and suggested to Justinian that there were problems with securing enough silk inexpensively enough through India, but that China was the only true source of silk, and investigations there might be valuable.
Justinian dispatched the monks (at least some of the same ones who had been to India) to China (probably overland this time, bypassing Persia to the north).
The monks managed to discover how silk was produced in China, and around 550 CE, they smuggled back either silkworm eggs, or young larvae, reportedly hidden in bamboo canes.
Presumably, they also smuggled back mulberry plants (as silk worms eat only these).
The Byzantines set up their own silk production (eventually in the Morea, in Greece, and in Anatolia) and began exporting silk across Europe and the middle east, breaking the Chinese monopoly (and the Persian trade monopoly).
The Byzantines both saved a lot of money by making their own silk, and earned a lot by exporting it. By the tenth century, however, the secrets of silk production had spread beyond their control as the town of Catanzaro in Calabria in Italy began producing silk, followed by many other places in Italy, and eventually Spain and France.
http://en.wikipedia.org/wiki/Silk
Eventually, the area around Lyon, France became the center of European silk production.