Does anybody know why capitalism a free-market economy?

Well, capitalism is not always a free-market economy.

A typical capitalism is a free-market economy, which means that the market itself (buyer and sellers) can decide the prizes and terms of services.

In capitalism, the capital is privately, and not state owned. But capitalism can also come in other forms: of social democracy with partially free market, and with other forms which include corporations having controls over the market.