Think of it in terms of this analogy: you eat too much, and so you've been gaining weight pretty much non-stop since you hit middle age. In the 80's, you ate too much and didn't exercise and put on 30 pounds. In the 90's you started exercising, but still ate too much and put on ten pounds. So, you conclude that exercising causes weight gain.
In a context like that, the silliness of the "reasoning" is clear. The exercising, if anything, seems to have slowed the weight gain. Similarly, the trade liberalization of the 90s coincided with a huge slowdown in the growth of income inequality, relative to the prior era.
Yes, but at least some meaningful part of the gains are going to others. Remember, in the Reagan/Bush years (which ended before NAFTA and the WTO were ratified), poverty ROSE, and real median incomes barely budged. Very nearly all of the gains were going to the 1%, back then. Then, in the Clinton years, poverty rates plummeted and real median incomes soared. The rich were getting richer, but at least others were, too.
Most educated people believe it's broadly beneficial. However, petty local lords don't like it, since it can undercut the kinds of people who were handed a million-dollar local business by their fathers, and who expected to be able to just go through the motions and remain rich indefinitely. Such people tend to be unaccustomed to challenges, since family money eased their path throughout their younger years. That left them ill-equipped to adapt to change. So, when global trade disrupts the status quo, that's a problem for them. People who developed more character growing up, by succeeding without family money, tend to see such disruptions as opportunities -- chances to find more efficient ways of doing things, which let them out-compete entrenched interests. But if you're one of those "entrenched interests," and you hate the idea of anything that forces you to think on your feet, changes like that will be terrifying. Thus, it's those small-town feudal lords who are consistently the epicenter of anti-free-trade sentiment. They want to throw walls up around their little kingdom so they can just keep going through the motions with daddy's money and stay rich. Disruption terrifies them.