Trying to discuss socialism in terms drawn from the capitalist ideology—whence terms like “own” and “property”—is not that easy. It’s like trying to discuss science using Biblical terminology.
Although you’ve never known anything else, the jargon of capitalism is not neutral.
The jargon you use is based on an ideology. In that ideology, working people are just another resource to be exploited. And thus the ideas that such terms represent are entirely foreign to socialism.
What we generally mean by “owning” is this: Using violence or the threat of it to exclude other people from using something valuable, for the life time of the person claiming exclusive rights. The owner class have set up institutions and systems—laws, police, courts—to normalise their violence and protect their ownership from their neighbours. Violence is normalised and institutionalised in capitalism.
By the way, this is also why capitalism has produced a discourse of “individual rights”. It’s fundamentally about the right of the owner class to own everything and their right to be the ruling class.
Socialists often emphasise our mutual obligations rather than our individual rights. And vest rulership in the collective.
The people who own things for a living and the people who work for a living tend to define “property” differently. The owning class require exclusive use of a good, because that is their livelihood and they make no other contribution. In this way, the thing owned becomes an “asset”. And
The socialist critique of capitalism is really centred around “property” in the sense of assets that fund the luxurious lifestyle of the owner class. We aren’t concerned with the tools of your trade, your clothing, or your knickknacks. Your stuff, your essentially worthless stuff, is yours, for all the good it will do you. Our focus is on assets and the system that the owner class have set up to protect their assets.
The working class tend not to own assets because the start-up costs are prohibitive. The owning class generally inherit their stake. For example, it used to be that working people could afford to buy a house with a mortgage - a long term loan in which one pays 100% or more of the cost of the house in interest, so the bank doubles their money with no work. This is what my father did (mother did not work and in those days that was affordable). But this is being taken away in order to fund more billionaires. And keep in mind that one autistic American billionaire just spent $250 million to help get Trump elected and thus get a seat at the table deciding how the violence of the state will be employed against citizens.
So most of the stuff that the worker class “own” is not the same kind of “property” because they can derive no income from it. Indeed, for non-asset goods the value usually declines over time.
For most socialists, certain things that are currently considered “property”, are thought of differently. Land is not something one can legitimately “own” for example. As a socialist society we would collectively negotiate the best use of the land. And we might divide it up, on a temporary basis, between people based on need and capacity. One may have exclusive access to land only by the consent of everyone. And it would be nuts not to grant exclusive use to farmers, for example, because they need it to grow food. But it would mean that incompetent farmers might be moved on to some other form of livelihood, by general agreement.
Just as the land itself is a good whose exploitation should benefit everyone. Similarly with what comes out of the land. Things such as oil, minerals, and diamonds cannot be legitimately owned by anyone merely on the basis of their willingness to use violence or the violence inherent in the system to exclude others.
These things exist whether someone owns them or not. And simply owning them contributes nothing to society. Indeed, exclusive ownership of assets is generally to detriment of the society. In the USA, for example, some 44 million live in poverty. Some 26 million don’t have any health insurance. And some 2 million people are incarcerated (the highest proportion in the industrialised world). All this in the richest country in the world.
In capitalism, people have no value unless they work to make the owner class richer. And since they are only ever willing to pay the minimum, for working people capitalism is a race to the bottom. At the end of the game of Monopoly, one person owns everything and everyone else is dead. It’s a quite a vision of society.
In socialism, the owner class make no contribution to society despite their evident capacity to do so. Therefore, they should get no benefit from society. And society should definitely not agree to their having exclusive access to a vast hoard of wealth while their neighbours starve or die of treatable illnesses.