What people generally misunderstand is what the phrase, "free trade produces the best result as compared to protectionist systems" really means. In the super-large, super-macroeconomic sense of global trade, this would be true, assuming everyone were producing at maximum capacity and supply and demand were in equilibrium. However, this is not the case, as any empirical economist will tell you.
The more important question is, "who is 'free' trade good for?" Any good student of economics knows that there is no such thing as a free lunch. Free trade might be good for an electronics trader in Japan who invests primarily in domestic industry, because in absence of tariffs, Japanese electronics companies are going to increase their revenues substantially because they have a competitive advantage. The same may not be true for an auto-worker in Michigan, who suddenly finds his skill set obsolete. Enormous macroeconomic forces driven mostly by university studies, government policies, and boardroom decisions largely affect the fortunes of the middle and lower classes, some without the benefit of a social safety net. In almost all allegedly "free" trade agreements, there are winners and losers. If you mean that the greatest good for the greatest number will be achieved through unrestricted flows of goods and services, you are right on two conditions.
1. You accept utilitarianism, or some form of political economy consequentialism, as the best ethical system.
2. You define "the good" as productivity.
Both propositions are debatable. Economics as understood by the average undergraduate does not tackle this reality. Sadly, most doctoral students in Economics are far better mathematicians and theorists than students of history and empirical data in economics. Empiricist Economists as a dying breed, and heterodox economists have found it harder and harder to find publishing and tenure opportunities in the face of the dogma now set up in North American universities. Read a book like Two Faces of Liberalism, No Logo, or Bad Samaritans and you will see that the discipline of economics is a lot grittier than the pretty two line graphs that most of us dealt with during our undergraduate studies in intermediate micro/macro theory. The way economics is taught now demands the memorization of certain canon "facts" like "free trade produces the best result," "minimum wage results in unemployment," "unions raise the unemployment rate," and "businesses operate by trying to maximize profits and utilize all available information to make a rational decision." Anyone who scratches beneath the surface layer of these propositions will find a story that doesn't fit well into easily categorized and cataloged sets of data.
In general, "free trade" in the NAFTA/WTO sense of the word benefits a few groups. First, it benefits the consumer class in wealthy industrialized countries who can buy goods at much cheaper rates. Second, it benefits large multinational corporations who have the assets and capital to seek out markets to produce their goods, ship them back to wealthy countries, and pad their bottom line. Free trade has not been so good to low-skilled workers in North America, small farmers in Latin America, or young girls in Southeast Asia (the latter is chronically subjected to classic "sweat shop" working conditions). Most people are either unaware of this, vehemently deny it is the case, or wring their hands and decide that it's ultimately better for "everyone."
One historical fact almost every proponent of "free trade" overlooks is that no country since the industrial revolution has built a successful domestic industry without a large degree of both subsidization and protectionism. Only after Western economies became established was the doctrine of free trade considered to be "correct" in the academic sense, largely because it IS better for those countries that already have strong domestic industries or sufficient capital to support economic colonization.