Why do 9/11 conspiracy theorists disbelieve the official story?

There are several reasons, most have been covered in other answers. I will give my own:

  1. The transnational group you are talking about, Al Qaida, denied responsibility for the attack at first, and the then-current evidence that it claimed responsibility was obviously fabricated.
  2. The physics of WTC towers collapsing is implausible, the physics of WTC building 7 collapse is just plain impossible.
  3. The planes don't look like jetliners--- the first plane is small, the second plane looks more like a drone, both to eyewitnesses and also in video images.
  4. There was a string of obvious fabrications, including the "let's roll" story, and the passports of the hijackers miraculously found in the debris.
  5. There was a simultaneous exercise dealing with the same events on the same day.

Point 5 is most important, because it allows a small conspiracy. To build drones that resemble jetliners and fly them around on the day of 9/11 would ordinarily take a bunch of people, and they can't all be in on the conspiracy, or else they would never go along with it, and someone would talk. But they would have no problem building such drones for an exercise, for the purpose of shooting them down, and they wouldn't even bat an eye if their exercise turned out to be so precient, that an actual attack just the same as their simulation happened on the very day of the simulation. They would chaulk it up to synchronicity.

The official story is not possible, it's ridiculous. But the requirement of a large conspiracy makes it difficult to believe anything else. The simultaneous exercises means that there is no large conspiracy required.

The simultaneous drill has been a recurring feature of attacks since, repeating on the London bombing attacks (where the people involved were startled when their exercise suddenly turned into a real attack), and most recently in the Boston marathon bombing. The sheer statistical improbability of the coincidence is sufficient evidence of a conspiracy, and the coinciding drill is the mechanism that allows the attack to be staged from the inside.

No drill, no attack. You can't get an army of inside people to attack their own country. But you can get them to pretend to, for a drill, and you can change this into reality with only a small number of people.