>The origin countries may have logistical difficulties with certain types of things which would otherwise go into a landfill. Throw one shirt into the landfill? Fine. Bring dump-trucks of clothes? Maybe now we have a problem. Same for E-waste (also an issue here in the form of used computers which are barely usable.)
I don't think there's anything special about clothes that make them particularly hard to dispose of, unlike e-waste. My municipality has warnings specifically for e-waste, but none for clothing. The non-cynical view of why we ship ewaste and/or clothes to china is that they're valuable on net, even if 80% of it or whatever are thrown away. You see this with e-waste. They're not just imported into the country and then dumped in the nearest river/landfill. They're sent to a recycling center where scavengers pick through them to recover what's left.