> What are you talking about? Bin Laden took credit for 9/11 immediately
Both my recollection and Wikipedia (admittedly neither being authoritative) agree that Bin Laden denied involvement for some time after the attacks (Wiki says he didn't claim responsibility until 2004). The Taliban denounced the attacks the day of and, separately, stated Bin Laden wasn't involved (which might seem weird, but there's some background there that makes it less suspicious than it seems, though of course it could have all been deception). They also volunteered that they'd turn him over if we turned up evidence that he'd been involved, on Sept. 13th (again, of course they could have been lying or stalling, just getting the events/statements straight)
The US demand (Sept. 14th) wasn't that they hand over Bin Laden, it was that they hand over all of Al Qaeda in their territory, all their intelligence on them, and Bin Laden. Given that there were a lot of fighters on their side of the civil war who'd been through Al Qaeda camps, this was probably impossible to do without losing the civil war, between the loss of manpower, the risk (I'd hazard it was a near-certainty) of opening a new and dangerously ill-defined front in the civil war, and the loss of said training resources/facilities. It was never going to happen, and we'd been considering covertly or overtly pitching in with the other side of their civil war for a few months prior (that part I didn't know until just a few minutes ago) anyway.
[EDIT] reading over the sequence of events and the public statements of both sides the Taliban comes off as even more reasonable than I remember them seeming at the time, which was already "fairly reasonable". Could have all been lies, of course, but if you just look at the public statements and the timeline of events—how quickly it escalated—just, wow. At the very least it was terrible PR management on the US' part that we came off looking like unhinged lunatics compared with such genuine shitbags as the Taliban.