For the FBI to be Constitutional an authorization for it would have to appear in the Constitution. Since most who know the Constitution well know that there is no federal police power of any kind authorized in the Constitution, that's all that need be written here. There are no implied powers in the Constitution, John Marshal's creation of them out of whole cloth notwithstanding.
Then by your argument, there can be no executive departments because there are none specifically named. No department of defense, no CIA, no NSA. There also can be no judicial review, thus the supreme court can't rule on the constitutionality of laws.
Of course this begs the question of who is supposed to enforce federal laws if there can be no federal enforcement agency. Those darned framers included that darned necessary and proper clause as well, which your position ignores as well. Being able to enforce a law is certianly necessary in order to carry it out.
If the FBI doesn't spy, then how did they get all those reports that they subsequently ignored about Arab men learning to take off, but not land 767's? That my friend is intelligence gathering. A euphamism for gathering intelligence is....
Give me a break. If you don't know the difference between an investigation and "spying" then I can't help you. There are hundreds of valid ways to figure out arabs are taking flying lessons.
The seven articles of the Constitution give precise details of what the Federal Government CAN do. The 10th Amendment gives all other powers not in the Constitution to the States or People respectively. Therefore- The FBI, not having any constitutional basis to exist, is by its very existence and activities, unconstitutional.
You won't find anything in article 1 about the executive department. The FBI is an executive agency. The CIA isn't specifically mentioned either. I guess thats unconstitutional as well. Why don't you poke your nose in article 2 and see what it says about executive departments.