Let this system expand at all, let people use it enough, and there will swiftly and predictably come a point where there aren't lots of untagged resources nearby for somebody to tag in society's eyes.
Once there are not plenty of new plots of land to tag and farm, people may indeed begin to ask, 'Why should this land be owned by them and not me?'
Because they did some work on that land? If that's the rule, then won't people who foresee the predictable scarcity later, run around trying to plow small shallow furrows through every potential field within the reach of running, trying to tag as much land as pointing to themselves as possible?
And when all that land has been used up, wouldn't the people who were slower runners and didn't end up with any land - wouldn't new children born into this world, for that matter - ask themselves and perhaps ask out loud:
"If this elaborate imaginary social construct doesn't offer me any benefits for going along with the pretense - if the system says that little or nothing has an imaginary tag pointing to me - then in what sense is this even coordination, from my perspective? Why would I cooperate in the coordinated rule of not eating things tagged as pointing to others, if the result is that there's nothing for me to eat? Where's my fair share of the rewards for playing along with this pretend game, for cooperating with what this imaginary tagging system says is my part and my action in it?"