It's my recollection that it was very well designed in almost every way aside from appearance. As in, the creature comforts were good, considerations for rear loading, ease of access, reasonable performance, etc. Unfortunately, when it comes down to it, people really make their vehicle buying decision based upon appearance. They may use a few requirements to pare down the field (e.g. AWD, four doors), but after that it's mostly looks.
I own several ugly vehicles (a T&C minivan for one). I wouldn't have touched an Aztek at the time with stolen money.
It looks cheap. Its front is a single molded piece of cheap plastic that goes from the undercarriage to the hood. It is surrounded on all sides by more cheap looking plastic bits. GM is infamous for putting cheap plastic bits on their cars that simply don't stand up to the elements; so anyone who has ever owned a GM car knows what an Aztek is going to look like after the warranty period is over. As it turns out GM must have improved thier plastics and the Aztek has aged well. But there was no way to look at one when it was new and tell that it wouldn't crumble like an old milk jug after six or eight years in the sun.
Is the appearance really all that bad either? I don't love it, but I've seen plenty of slightly awkward-looking cars and I'm not sure what's supposed to make this one so particularly bad. Maybe the photo in the article is from an unusually flattering angle?
In both of the pics in TFA, the camera is on the ground, so we're looking up at the vehicle. That's kind of an old trick for making any mostly-horizontal object look better. The truly awful angle from which to view an Aztek [really, has no one complained about the spelling of this name?] is from the back.
They actually look worse in person. The first time I saw one of these on the road, my jaw dropped - I just couldn't believe that something this unlovable made it into production. I distinctly remember thinking "GM has gone seriously off the rails". And this is coming from someone that owns a KTM 990A and a Honda Element!
It is quite a bit different than the aesthetics of vehicles that were out at the time. It fits a lot better with current aesthetics with the rise of the crossover than it did a decade ago.