It's a philosophically coherent argument. We won't own people. We draw the line there. Many indigenous cultures don't and never really have believed land can be owned. You don't have to agree with them about that but you also can't dismiss the concept out of hand. And if people can't be owned, and maybe land can't be owned, it's not clear anything necessarily must be able to be owned. Are animals owned? Are plants owned? Are rocks owned? Largely, yes. But who allowed that? We did.

The idea of private property is an almost uniquely human idea, we have based most of our system of civilization on it, but it is not universal and is not based on any physical laws that we know of. We just like to own stuff, and we kill anyone who won't let us or tries to tell us we don't. And the fundamental corollary of that is that if we exclusively own something and get to decide who can and cannot have or use that thing, then that ability is deprived from everyone and everything else who is no longer able to exercise all of those rights over that thing. Sometimes that is a good thing. The tragedy of the commons demonstrates how things owned in common or public use can become quickly destroyed. By having exclusive ownership, perhaps I will do a better job of taking care of said thing and can protect it from careless use or overuse by others. Ownership can be a powerful idea, giving people equity in things that they would otherwise not be as invested in.

Strictly speaking though, property is theft. Theft from the public domain. It's taking something out of the public domain where it naturally started, and claiming exclusive use and ownership of it on behalf of one person or group or organization, often dating back through a long series of transactions, some incredibly violent, deep into ancient history, but at the very beginning of that chain of ownership you'll inevitably find someone using some justification like "I/we found this first" which in any given case may not actually be true, but the claim is made regardless and then used as a justification for making something private and exclusive for no reason other than that they could, and no one else was around or willing and able to stop them. Nothing and nobody gave the Earth to humankind -- we took it, and divided it up amongst ourselves and continue to do so to this day. And that's good for us, being ambitious and greedy has been good for our species in many ways, although it has also caused great strife and horror. But let's be intellectually honest about what property rights really are and why we have them. I still think they're mostly good, but I can also understand the point of view of people who think they're not, or that they should be limited.

Re 1 & 2, just because there are differences and conflicts does not mean they are unmanageable or irreconcilable.

3 is just sounding no-true-Scotsman.