I believe that this is egocentrism. Anybody watching two dogs fight over a possession know that they understand "mine". This is an instinct.You choose to interpret that instinct/reflex as "property". That is your interpretation, not mine. I find yours stretched to the point of near absurdity, frankly.
Territoriality and assertion of status are instinctive. Property is not. Even posession is not, except as an expression of territoriality and status. Property is a social construct the purpose of which is to help regulate and mitigate conflict over territory and status.
Believing that their social structure was not created to protect possessions from being taken, I believe is more egocentrism.
Humans want to believe that all things are special to them. Some things are. We create greater societies and increase protections for property, but the establishment of societies to protect property is not unique to the human animal.