The answer is simple. Imagine how successful your manufacturing union would be if it had a monopoly on manufacturing labor within your state. Now imagine how successful it would be if your employer couldn't sell the products you manufactured to anyone outside your state.
Free trade gives American companies access to markets to sell their products, and it gives citizens (and not just those lucky enough to be in a union), access to products that would normally be more expensive if they were forced to buy from a monopoly (either on labor or on capital).
That argument is strong enough that 87.5% (in other words, a supermajority of economists on both the right and left) would abolish trade restrictions altogether if they had their way. http://ew-econ.typepad.fr/articleAEAsurvey.pdf