Here's my non tinfoil quasi-edumacated guess: back in the mid-80s someone or some group tried to get the building reviewed to see if it had merit as a historic building - but due to more pressing issues and more impressive competition nothing happened.
Insert several decades, add damage from parts of a 9-11 plane falling through the roof (that CAN'T have improved it), changing tenants, economic downturn, and finally a client with money to knock down the existing (and my guess rather run down building) and build a new project with both the Mayor's and neighborhood's approval.
The building does have some semi-interesting history and architecture associated with it, but it's mainly the same general history as the rest of the neighborhood and that is not exactly a compelling architectural or economic reason to keep it. The petition submitted makes some very general and broad claims, but lacks the kind of factual historical data and elements typical of approved projects.
Yes, there is a historical neighborhood nearby, the building is of an age and nice enough design that makes me wish they could remodel it, had some interesting tenants, and it was affected by 9-11, but that is true of many buildings.
Now, if there was a benefactor for the building who wanted to buy it, restore it, and enter it on the Historic Register, that would be different - but there hasn't been such a person/group for decades.
I don't think this building has been treated any differently than the vast majority of structures put before the Landmarks Commission and the fact that it is CURRENTLY in use as a Muslim Prayer center speaks volumes about reality vs. media sensationalism and political punditry.