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Saying you support capitalism doesn't make you a capitalist. That would be like saying support monarchies makes you a monarch. Many people also confuse capitalism with free markets which are actually two different things.
Capitalism is where the wealthy use their wealth to create wealth, which isn't a bad thing. The problem becomes wealth inequality where free markets are no longer consumer driven. Even if someone tries to enter a certain market the capitalist can drive them out by operating at a loss until they become a monopoly again and this has happened often.
A great example of this is the housing market. It's impossible to find starter homes at reasonable prices because manufacturers stopped building them so that people looking to buy a house would have to buy a more expensive one and because of the scarcity of starter homes the price on the few existing ones skyrocketed as well. This forced people to instead rent, which means they're no longer building equity in their house. Then the rental real estate company uses that capital to buy up more houses which drives the price of houses up even more so they can justify jacking up the cost of rent on houses they already own and can turn around and buy more houses and repeat the cycle. This also causes the price of renting apartments to go up because they can justify hiking the price because of the cost of renting. Who owns the apartment complexes? The same real estate company that's buying all the available houses on the market. The cycle is repeated until workers can no longer afford a place to live.