In his press conference last Friday, when asked by ABC News’ Jonathan Karl to defend previous claims that Al Qaeda has been “decimated” and is “on the run,” President Barack Obama replied that while local affiliates were active, the U.S. had largely defeated “core” Al Qaeda. It was a misleading answer, because Al Qaeda was always designed as an umbrella group to support separate local terrorist organizations.

The very term “al qaeda” means “the base.” Osama bin Laden and his lieutenants sought to provide a basic foundation of training, funding, and inspiration to Islamic terrorists throughout the world. The idea–largely successful–was to franchise terrorism to local affiliates, guiding attacks loosely. It is therefore meaningless to dismiss attacks across North Africa and the Middle East as peripheral; that is Al Qaeda’s business model.

A charitable way of putting the Obama administration’s theory is that Al Qaeda is like a supernova: what we see through a telescope is the spectacular wave of debris radiating outward from where a large star used to be, but in the end everything will dissipate or collapse. The alternative is that what we are seeing is not a supernova, but a nebula where new stars are being formed (yes, some nebulae are formed by supernovas).

It is difficult to know precisely what is happening to Al Qaeda, but it is certainly not yet defeated, and the illusion that killing Osama bin Laden and other leaders is sufficient is a dangerous, complacent notion. That is especially true when, at the moment, the Obama administration is boosting the Al Qaeda-dominated Syrian opposition forces. How can it be receding, when the Obama administration’s policy is to arm it?