When people from different countries are allowed to trade with one another, the cultural differences between them get eroded. As they trade with one another they exchange elements of their cultures, ranging from how they do business to how they pack goods to how they interact with one another on the phone. This highlights the arbitrary nature of borders and helps bring different people together, which promotes cultural understanding.
Free trade makes war less tasteful. This is partly because of cultural cohesion -- the better you can relate to people on the other side of a border, the less-inclined you will be to shoot at them. Just as important, though, is the fact that free trade makes war less economically viable. Invading a country that you freely trade with is cutting off access to markets, customers, raw materials and suppliers, all of which could benefit your country in peacetime but can do nothing for it in wartime.
Free trade allows people to make their own choices. If you want to buy a car, free trade allows you to buy it from an American, Japanese or German company. This is part of your right to life, liberty and the pursuit of happiness, and if restrictions are placed on what you can buy then this right is being impinged upon.
Free trade lets people freely interact with and deal with more people than they would in a restricted trade setting. This in turn encourages them to trust one another; this builds social capital, which is when people interact with and trust others outside their immediate family. A society with more social capital can do more with less, functioning with fewer laws, regulations and people to enforce them, which makes it richer and generally better off. While free trade isn't the only way to build social capital, it is one key way to do so.