Free market is not capitalism. You can have capitalism without free markets (in fact, capitalism exist outside of free market most of the time). The origin idea of libertarianism, probably the most pro free-market ideology, is anti-capitalist, and hate the idea of LLC, which is anti free-market, and pro-capitalism.
Can you go into more detail here? My understanding is that a free market requires capitalism (privately owned wealth) to function. And capitalism needs free-ish markets to actually use the wealth.
I'm also unsure how libertarianism is anti-capitalist.
Capitalism is about who own and decide what will be produced: the capital owners (it can be the State, like in China). In a free market, the market itself decide what will be produced, as all agents have full, unaltered information.
US libertarians came from individualist anarchists, who basically thought that under capitalism, volontary exchange could not exist, as wage workers could be forced to work by power imbalance created by capitalism.
Even some neo classical liberals (liberalism is the ideology promoting free market) have played with the idea of natural monopolies created by land use. Hence you will see a lot of georgists amongst liberals who really thought about a perfect free market capitalism.
Finally, a good critique of free-market socialism (where every company is employee-owned, with real liability) is that interest groups will still form and lobby the government for advantages, distorting the free market, like the asset owners do currently (hence it cannot work in a representative democracy).
Capitalism is a system composed of many agents with conflicting wants.
A lot of the capital owning capitalists would prefer the markets to be less free in many ways. If I own a toll road, I really don't want a parallel toll road. This sounds like a ridiculous allowance in a capitalist system but look up the Ambassador Bridge. It is very much in that owner's interest for the market to not be free at all.
If you look at lobbying, many capitalists advocate for less free markets all the time. I'm not just talking about the capital owners either. Labor advocates push for less freedom in the markets consistently through wage floors and legal restrictions on employers.
It seems like there is an equilibrium point where a completely free (meaning every person for himself) devolves to the point where the lack of trust becomes too high of a transactional cost. Both food producers and food consumers benefit from regulations that don't allow you to sell sawdust disguised as flour just because you are able to convince someone that it will work the same.
