Based on chemical reactions involved,

The action of U.V rays causes the dissociation of chlorofluorocarbons to release the free chlorine radicle

CF2Cl2 + U V radiations → Cl + CFC

Now this Chlorine radicle so formed is free and in the stratospheric layer reacts with the Ozone to form Chlorine monoxide and oxygen

Cl (g) +O3 (g) → ClO (g)+O2(g)

chlorine monoxide reacts with the nascent oxygen and free radical of chlorine is formed.

ClO (g) + O (g) →Cl + O2

Chlorine radicles are being regenerated in this way and are reacting with the ozone layer. So, CFCs are considered as the source of chlorine radicles which are destroying the ozone layer of the stratosphere.