Trying to be charitable, I think maybe it's just a cultural thing. If someone grew up immersed in a culture which tells them that walking everywhere is a natural right of man, then it wouldn't be surprising if they think of private land ownership as being heinous. It's a very alien view to me, but values shaped by culture generally are. It's just how it is.
I think the claim is more like: "We grew up in a culture that forgot how the freedom to go everywhere ought to be something we value. I have remembered that this is a good thing to value, and you should too."
Many countries allow private land ownership, but also have a right to roam; the land ownership is qualified (as indeed almost all land ownership is nearly everywhere; that's how eminent domain works).
If you were to ever try to create a new railway, or even a small hiking trail along an existing body of water, you will discover it would have been much easier centuries ago before the local municipalities gave away all the land. It is a hard thing to undo, is the point. You wish you could go back in time and set aside the necessary land for trails, parks, etc.
For some people freedom means being able to violently deny others to roam the land, to deny access lakes, to deny foraging for berries and mushrooms and even to deny them access to the coastline and the ocean.
For them, freedom might entail being able to deny these basic modes of being e.g. based on monetary worth, social standing or even ethnicity (like country clubs in the US).
If that's what you consider freedom, I don't think I'm going to be able to convince you otherwise.
I already explained what I meant by damage. Being unable to see how the freedom of a tiny minority shouldn't trump the freedom of basic modes of being of the vast majority, that's damage.
"repairing the damage caused by centuries of private land ownership."