There are three big reasons not to think there's been a conspiracy by people powerful positions in the West behind this whole thing.
1) "They couldn't be that wicked"
2) "They couldn't hope to get away with it"
3) "The suicide hi-jackers couldn't have been in on it."
And there is one big reason that goes in the other arm of the scale. The principle of Cui Bono. In any crime, suspect the people who stand to benefit most from it.
So far as "They couldn't be that wicked" goes, that's very open to question. More civilians have been killed in the attacks on Afghanistan than were killed on 9/11. Nuclear deterrence means an agreement in principle to kill millions of civilians.
So far as "They couldn't hope to get away with it" goes, that doesn't necessarily stand up. The very scale of what happened on 9/11 means that any suggestion of a conspiracy is almost certain to be dismissed as crazy. If there was such a conspiracy against America by people close to the levers of power, and someone ever broke ranks, they would never be believed by anyone, apart from a rabble of conspiracy nuts.
And as for "The suicide hi-jackers couldn't have been in on it", while that is perfectly true, it is not necessarily relevant. It would just mean that intermediaries who thought along those lines had been recruited and guided along to do the actual dirty work. That's been done often enough, on a smaller scale.
That doesn't mean a conspiracy is proved. It just means that it can't be dismissed out of hand. And when all is said and done, we are never going to know.