It's crucial to understand that if we let a person that build a shelter keep it for eternity then that person can build many shelters such that there will be no land left for other people to build their shelters on.

Indeed.

This is why in a society free from theft, one must build or make something for exchange to get things you want.

I don't see why buying two plots and building two houses entitles someone else to one of them.

I don't agree with the notion of buying a plot. No one should ever have to pay for an empty plot of land.

OK, so you dont buy the plot and just build two houses on them. How does that change your logic.

How do you deal with a situation where some people don't have any land anymore to put their houses there?

They make something they can trade, or go somewhere where there is land.

How they can make something they can trade, if they have no land on which they can make it? Where can they go, if private property exists in most of the world?

You make things that don't need land, like 99% of humans on the planet. AKA get a job.

There's no free land, but there is cheap land, especially in deserts. Simply owning land might not be as nice as you imagine