It's really not a big deal why he doesn't. He doesn't because of inventory purposes (Hobby Lobby keeps no back stock). Here is a bit of info on it (found by a simple Google search)
Green’s detractors speculate that his Christian beliefs are behind the decision. They theorize that Green sees barcodes as the “mark of the beast” referred to in the book of Revelation in the Bible. Not surprisingly, a Google search on this topic returned hundreds of personal blogs, but no published articles.
So what’s really behind the decision? The decision partially stems from Hobby Lobby’s core value of emphasizing people over profits. Green never wants to send a message to his employees that conveys, “Instead of using you, I am going to use the computer to replenish your stores.” In his book, More Than a Hobby, Green insists that barcodes just don’t pay their way. Green maintains that employees know what’s on shelves and can better help customers if they take inventory the old-fashioned way, by counting. “The computer won’t know if products are broken or stolen”, he says. “It blithely goes on telling the staff they have such-and-such, when in fact they don’t.”