which you did not create?"
It can not be justified. What is created by man are border agreements and any bundle of rights created by man attaches to a border agreement (ie. treaty, deed, state constitution, etc.) not land.
Your question is a reason common law traditions included rights of way for land and water so long as they were traversed in a manner that did no harm. Your question is a reason Supreme Priests wearing black robes for the religion of biggest gangs said the right to travel is more sacred than a right of free speech the century preceding driver licensing.
RE: "If you break a rock, why are those pieces now yours?"
Libertarians argue they are justly yours based on property rights deriving from self ownership. You own your body, labor, and its fruit. You quoted Paine, I shall quote Locke:
Though the earth and all inferior creatures be common to all men, yet every man has a "property" in his own "person." This nobody has any right to but himself. The "labour" of his body and the "work" of his hands, we may say, are properly his. Whatsoever, then, he removes out of the state that Nature hath provided and left it in, he hath mixed his labour with it, and joined to it something that is his own, and thereby makes it his property. -Second Treatise of Government, 1690.
RE: "Why shouldn't someone else be able to pick them up? And hold onto them?"
Libertarians argue if they are abandoned then someone else is able to pick them up and hold onto them. However you don't see libertarians advocating legitimized biggest gangs ought to be legislating circumstances of abandonment which shift burden of proof liability or accountability of a trespass to a victim. Just because I go on a vacation for three months and you think my home is abandoned does not justify possession transferring to a trespasser and shifting any burden of proof for non-abandonment to me in order to get possession of my own home back because "possession is 9/10ths of the law."
RE: What right do you have from stopping a Natural Man from walking through "your property?"
None if he is merely traversing God's green earth and doing no harm while crossing territory of your recognized borders. Then you might come up with a lifeboat scenario and say ... what if I live in a community that has provided sidewalks for natural men to traverse territory but he insists upon cutting across my brand new grass? This is probably a reason there are legislatures establishing all manner of circumstances because people do not want any liability for wrongdoing when dealing with assholes. The dude was on my grass under these circumstances so I shot him and the statutes say that it is perfectly ok to kill assholes on your grass if there is a sidewalk available. I ran that dude on a bicycle over but because he is a poor asshole who can't afford lights this statute says I am not at fault or liable under those circumstances. Problem solved.
We do have an idea of what is right and good. Live as free men but do not use your freedom for evil, turn the other cheek, if someone forces you one mile go with them two, love thy enemy, etc. As a people we are just not down with right and good because if some asshole pisses us off our first response is typically more like screw you pal, who the hell do you think you are ...