Free traders base their "proof" on idealized models that don't reflect reality. They go back to variations on Ricardo's concept of comparative advantage as their evidence. On paper, it makes sense, if country A is better at producing X and country B is better at producing Y, why not have such a division of labor? The problem with this simple model is that it assumes that capital of country A and B remains in its respective country so that each goes on producing what they're most efficient at. What it doesn't consider is a scenario where cheap labor or other low overhead costs leads to a large-scale flow of capital from A to B, so that B winds up producing both X and Y while A is left with a service/finance sector economy and little else.
Free trade advocates also consistently ignore any and all empirical evidence from history that contradicts their models. They claim that tariffs and trade protection lead to economic stagnation. OK, that's a valid hypothesis, so let's test it against reality: the US economy was "protectionist" for much of the 19th Century, precisely the time during which we experienced the fastest relative growth in GDP in our history, and the time where we overtook the UK and the rest of Europe as the world's manufacturing superpower. So much for tariffs and trade protection leading to stagnation.
The IT side of this is often overlooked in free trade discussions. It's one thing to impose tariffs on manufactured products and raw materials, but it's damn near impossible to do anything to restrict the flow of information through electronic means.
Great post sir!