It is a natural thing to want to own the property you live on at least, even lions urinate on their turf to mark it as theirs. How would you start preventing humans from doing what every mammals has ever done ever?
As usually used, "private property" is a superset of "personal property", as all non-government-held (non-"public") property is " private property", including both real and personal property.
But I think you are probably using an unusual and ideologically-specific definition of "private property" that you should probably detail explicitly.
This all counts as personal property (though of course people disagree about what exactly should count as personal property). An example of private property is owning a factory that you don't personally work in, or even owning an apartment which you have never lived in and don't intend on living in. The Sauk leader Black Hawk articulated something like this idea when he said
My reason teaches me that land cannot be sold. The Great Spirit gave it to his children to live upon, and cultivate, as far as necessary for their subsistence; and so long as they occupy and cultivate it, they have the right to the soil—but if they voluntarily leave it, then any other people have a right to settle upon it. Nothing can be sold but such things as can be carried away.
Locke[1] also believed that people shouldn't be able to own things that they don't personally use or hoard resources if they are scarce.
What if you're the best at managing said factory without working in it, should I own it instead because I work there even though I have terrible management skills that will lead it to bankruptcy? Seems awfully inefficient. Should the people working at Apple factory own Apple? Not making much sense. How long would it last?
I think managing a factory counts as working in it (working in the office rather than on the floor). With respect to the idea that there should be no private property, it seems to me that there's no reason that this implies that a factory should be managed by factory workers. By all means hire managers to manage the factory, it's what they're best at. But managing a factory (i.e. being the person that coordinates the business side of the company) isn't the same thing as owning it or controlling it. You can imagine, for example, a factory that is managed by a manager but ultimately owned and controlled by a worker collective (which includes the manager). The most important decisions of the factory could be made democratically (supported by data gathered by managers) whereas the day to day business decisions would be made by people who manage the factory.
That wouldn't work though. Factory workers from a competing factory would attract the best managers by offering them more money or complete control and ownership because they know the factory would have way more profit and therefor more money for the workers this way. And then you're back to private property because it turns out its the most efficient way to get things done.