The Washington Post has a front page article telling readers that the debate over the Korean "free trade" agreement is actually "a dispute over free trade itself." The Korean trade agreement is not in fact a "free trade" agreement. It does not free trade in many areas, for example it does little to reduce barriers to trade for highly paid professional services, like doctors and lawyers' services. The deal also increases some barriers to trade, most notably by increasing copyright and patent protection.
The proponents of the deal use the term "free trade agreement," because "free" has a positive connotation which they hope will help sell the deal politically. They do not use the term because it is true.
Similarly, it is absurd to claim that the United States is having a "dispute over free trade itself." There are no prominent public figures who support free trade. Genuine free trade would eliminate barriers to trade in all goods and services. In areas where these barriers are greatest, like health care, free trade could have an enormous impact in improving living standards and reducing inequality since prices in the United States are so far out of line with prices in the rest of the world.
Instead, the trade agenda of the United States had been about reducing barriers to trade in manufactured goods with the purpose of putting non-college educated workers in direct competition with much lower paid workers in other countries. The predicted and actual result of this policy is to reduce the pay of non-college educated workers, thereby increasing inequality in the United States. This is a policy of one-sided protectionism. It has nothing to do with "free trade."