The phrase "old wineskins" means old or outdated ways of thinking, doing things, or organizing systems that are no longer effective or suitable for a changing environment or new ideas. Full definition
These are the parables of the wedding guests who need not fast while the bridegroom is with them; of putting a new patch on an old garment; and of putting new wine in old wineskins (Matt. (religion-online.org)
Nor do they put new wine into old wineskins, or else the wineskins break, the wine is spilled and the wineskins are ruined. (religion.blogs.cnn.com)