A free market system has both advantages and disadvantages. As you consider the virtues of a market economy, it is also necessary to look at how real world contexts limits these virtues.
In theory, free markets allow buyers and sellers the greatest amount of choice. This theory argues that quality will improve and prices decrease as a result. Buyers can seek out the best quality at the lowest prices. If someone can make a better or cheaper product they are free to do so. In the real world, though, very large companies can sell products below cost to bankrupt their competition and then raise prices again. An example of this was airline deregulation, which originally was intended to lower prices, but has led to the current situation of high prices, de facto monopolies, and worse service.
Next, a pure free market allows the maximum degree of freedom for consumers and producers of goods. On the positive side, this encourages innovation. On the negative side, this means, for example, that producers are free to sell adulterated food, not deal with pesky safety standards, sell drugs that are ineffective or even harmful, build schools that are fire hazards or otherwise harmful to children (using asbestos insulation, for example), build cars that explode, etc. A purely free, unregulated market offers no protections at all to consumers but it does maximize profits for producers.
Free markets are efficient. With no regulation, in theory, inefficient producers will fail and efficient ones thrive. This should prevent rent-seeking and the growth of sclerotic monopolies. In actual fact, though, monopolies and oligopolies are common in putatively free market economies, especially in the "winner-takes-all" case of platform or network products (e.g. Google, Amazon, Uber).
Most people believe that a market economy is the best economic system. There are a number of reasons for this. Let us look at three of them.
It offers the most freedom. It is important for people to be able to do whatever they want to do. A market system allows for this more than any other system. In a market system, the government does not really tell you what to do with your money or your property.
It offers the widest variety of goods and services for consumers to buy. In a market economy, companies will compete to offer consumers things to buy. The companies want to do this in order to make a profit. Therefore, they try to invent new things that customers will buy. This creates a huge variety of goods and services from which we can choose.
It offers the best quality of goods and services. The competition between companies mentioned in the previous paragraph does this as well. In a market system, companies continually try to offer the best quality (or the best combination of quality and price) that they can. They do this in order to get more customers. This allows us as consumers to get the best quality of goods at the lowest prices.