Here is the way I see it:
Accept that free trade as a general principal is a good thing for all parties.
NAFTA and agreements modeled after it have this in common:
They throw US manufacturing jobs under the bus so that we can all have more competitive, fuel efficient, cheaper, safer cars. (Hooray).
OK, so lets say we just killed ~2,000,000 'decent paying' jobs, many of them union, and did a number on hundreds of rust belt communities. Well thats fine, everyone is better off. We are saving money here. Saving Lives.
But what about other industries? Pharmaceuticals do not support nearly the number of jobs that auto industry does. Maybe 30,000 very well paying white collar jobs, people who are upwardly mobile and educated. It is widely accepted that that industry is sapping US economy of strength. We regularly pay 10X what other countries do. Why don't we open up that market to competition too!
Oh wait, thats an industry with deep connections in Washington. They rank up there with banks as the largest political donors, spend the most on lobbyists, and so on. So count them out, they don't need competition.
OK, so the standard counter argument to this is that Pharma is a special case. We let them keep the fat on their margins because... innovation! Think of all the lives we are saving by shoveling them money! If only it were that simple.
The overwhelming majority of the increase in lifespan over the past 100 years has not been modern medicine; its been public health efforts like sewars, safety standards, and as well as a handful of fluke cures like polio vaccine, penicillin, smallpox vaccine, no thanks to the pharmaceutical industrial complex.
I could go on, the point is that too often trade deals are structured to protect the politically connected and their interests while regressively opening up high employment industries to competition. So even if you believe that free trade is a great thing (I do) it is also valid to acknowledge that it has historically been adopted in a regressive way.
Medicine is by far the most flagrant example, but plenty of others.
Another valid, if more contrived argument is this: A trade agreement is a treaty. Once a treaty is passed, congress cannot easily change it; it become the domain of the executive branch and regulatory agencies specified in the treaty. So a lot of progressive critics see it as a way of creating a court system to mediate trade disputes which is not accountable to the laws that congress makes or repeals.
On example of this is the cigarette industry, which has successfully used NAFTA courts to prevent third word countries from banning sales or making labeling requirements on the grounds that it was a violation of IP and so on.
But the bigger problem is that you have this international body making decisions that effect everyone which is not directly accountable to anyone. So in its way it is a separation of powers and taxation without representation type argument which really requires deeper reading than I can provide here.