For the sake of argument, let’s say that Amazon makes up 50% of UPS’s business, and those packages are shipped by UPS at a 10% loss. If the other 50% of their business averages a 20% profit, then they’re averaging a 10% profit across the board.

Without the Amazon packages, let’s say UPS can cut their operating costs by 25%. Now they’re shipping 50% as many packages, though, so the per-package operating cost has increased by about ~33%. Those customers that were generating 20% profit when the network was larger are now a losing proposition. UPS then faces the choice of downsizing their operation or raising prices. Both of those options are about equally bad when you consider that their competitors are not impacted by the loss of Amazon’s business (well, to be totally correct, their competitors have already absorbed the disruption to their operations when Amazon pulled their business to move it to UPS in the first place).

To be clear, I’m not saying the above numbers are correct - or even close to being representative. I’m merely illustrating why it makes sense for transportation companies to take large-volume customers even at a loss.