Why would Osama DENY involvement in 9/11 ?

This question has been bothering me since 9/11 happened.

While growing up, and even now, I have noticed that, whenever there is a terrorist attack, every time, within a couple of days, we hear some terrorist group 'claim' that they were responsible for the event. It is almost like, they are eager to be credited for the event...

So, given this trend, and given the magnitude of 9/11, if Osama was in fact responsible for 9/11, far from denying his involvement, I would have expected him to trumpet it as a great achievement of his....