This really goes back even further to the fall of man. Death created desperation, survival, reliance on security, false peace that life was better if you lived in comfort (and therefore, you wouldn't dwell as much on Death). And in gathering all of these things, we create more sins.. Like crushing other men, living in hedonism, creating barriers from your fellow man, because he also wants your stuff.
This is the true meaning of original sin. That it first brought Death - and Death, in turn, brought in more sins. And it's also why Paul says the love of money is the root of all evil. Original Sin is not some mystical genetic trait, but something that streams from death. Conversely, Christ is the new Adam who introduces the paradigm of Life - and remakes the world in his image rather than Adam's. Our own actions and notion of property should reflect this joy in Life as well (rather than reflect the fear of Death), the more and more we abide with Christ.
That's not to say property itself is bad for a Christian. It's just that we should be living in a transition stage now, where we are made new. We are not heavenly beings as of yet - "We see in a glass darkly" - but we are called to live in the Spirit and not the flesh. We should always keep in mind that the things of the flesh will pass away, and not be stubborn in sharing or parting with them if it helps someone. As Jesus said, give your cloak to someone in need. And don't live in anxiety about what you'll eat or how you'll dress. The pagans worry about things. But "seek first the kingdom of God and his righteousness and all these things shall be given to you".