Owning things becomes important when you have an internal void. When your internal world is deprived it is only natural to want to fill it with external things. Unfortunately, this is like filling a sieve with sand. The sand may fit in the sieve temporarily, but it will soon sift through the holes, leaving you empty again.
What do you fill that internal void with? Here are a few aspects that fill the void better than possessions:
Relationships
Passionate Work
Service to Others
Personal Challenges
Knowledge