In Captain America: The Winter Soldier, Nick Fury has reservations regarding Project Insight, and expresses those concerns to Alexander Pierce Fury asks Pierce to delay Project Insight, and Pierce says that he will.
Immediately afterwards (or at least, in Fury's next scene),
there is an attempt on Fury's life, orchestrated by Pierce and HYDRA.
When Pierce speaks to the World Security Council later on, they mention that Project Insight had been delayed on Pierce's insistence, based on Fury's request.
Pierce was really HYDRA, and he put the hit out on Fury's life pretty much immediately...
Why did Pierce bother approving the delay, or telling the Council that it had been delayed?