I like to ask that question. The best answers I've gotten involve a different president invading Afghanistan - but doing the follow up better and not invading Iraq and somehow keeping Saddam in a box, as the UN fell apart.

The president could have waited longer.

His/her argument could been we will get the people who were responsible for 911 but we would approach the problem systematically [or say a number of other perhaps better excuses].
So, instead of invading Afghanistan within 6 months, it could have instead taken year or two to start it.

Delaying any military action should have many advantages.
First it would cost less money.
Second, one could ask for a larger military and get a larger military than our current one. And trained people or got more people with foreign language skills.
Third, you might give more time for other countries to respond- and response may have been things other than troops sent somewhere- their leaders could make speeches and change policy.

By waiting longer, one is creating a political vacuum in which world leaders will be drawn.
One also would lessen the significant of 911 attack and one could spend more time mourning the dead from 911.

By acting quickly, you are letting other world leaders off the hook- the Americans doing something about it, they have the better military and tons of resources, etc.

By delaying, one might get some international definition of what terrorism is, and what national policies could enacted to combat it.

So, to make clear the president needs say action will be taken against 911, but delay any quick response. You could say our quick response was a product of the Cold war and there was no real advantage to moving quickly in this situation.