I'd say the best explanation for the backlash is that the move was unilateral. Not only were UEFA and Fifa left in the dark, but also the fans, the managers, and the teams. If they had instead proposed a consultation along the same lines, the backlash would at least not nearly been as intense. But a fait accompli, coupled with incredible timing (Uefa announced reforms to the Champions' League that these clubs had agreed to, and then walked away from it); and, apparently, lying to other organisations that they'd have needed to work with, went down exactly as well as such things always do.
Moreover, it's against the rules of the national leagues to join another organisation. So there's a level of arrogance to it as well, the entitlement of these clubs thinking that they deserve by default to be represented at the top of the game and thinking that every other authority should just roll over and accept it.
So it was badly handled. And predictably so. Which makes it also monumentally stupid.