People have always traded, since the earliest pre-human artifacts. Trade makes both sides wealthier. Outlaw property rights and people will use other mechanisms to defend their property.
What the parent comment says is not to outlaw property rights absolutely, read the comment again "private ownership of land or large businesses", it's a very specific subset of ownership.
Trading and markets are not the problem. Unbounded accumulation of capital is. Capitalism is actually anti-free-trade and anti-free-markets because it creates a positive feedback loop where the more capital you have, the more economic rent you can extract from others, which can then be used to grow the capital. At the end of that loop is a degenerate market dominated by a single monopoly or a few oligopolies, not free in any meaningful sense.
Therefore, if society wants free trade and free markets, it needs to prevent this. And the easiest way to do so is by making unbounded capital accumulation impossible, by refusing to acknowledge it as legitimate property right past a certain point, and thus withholding society's protections for it. It doesn't mean that all property rights are gone.
There is no such thing as "rent extraction" in a free market. I am gaining capital because I am serving others well, so they voluntarily give me their money. Trade is not zero-sum, we are both better. Capital I accumulate is reinvested, or spent on things I want. There is no problem with capital accumulation.
You have come to the exactly incorrect conclusions