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Animals can do that too. The problem isnt with opening bag and getting a thing out. The problem is a concept of possessing a thing. In anime, a few pokemon actually posses anything. But even those that do, liek Braixen, they understanding of it is more simple, like, "its a stick I get used to do limited amount of things with". Bag, as a concept, isnt just a box you put things and take out, it carries valuables you are attached to or require: a pretty rock you lie, your wallet, may be a brush, notebook, etc. Each of them have meaning for you and it becomes a complex object, not just something that challenges your physical capabilities to interact with it.
As a human you grew up with the idea you carry purse (or use pockets) and even when you leave specific place you automatically check if it is with you. This is something that you learn as you grow up, it becomes part of you.
