In fact, the Constitution says no such thing. And, it doesn't say you can't be fired for insubordination by the FBI. The applicable law is found in Chapter 18, Paragraph 2385 of the United States Code. Among other things, it says: "Whoever knowingly or willfully advocates, abets, advises, or teaches the duty, necessity, desirability, or propriety of overthrowing or destroying the government of the United States or the government of any State, Territory, District or Possession thereof, or the government of any political subdivision therein, by force or violence, or by the assassination of any officer of any such government; or
Whoever, with intent to cause the overthrow or destruction of any such government, prints, publishes, edits, issues, circulates, sells, distributes, or publicly displays any written or printed matter advocating, advising, or teaching the duty, necessity, desirability, or propriety of overthrowing or destroying any government in the United States by force or violence, or attempts to do so; or
Whoever organizes or helps or attempts to organize any society, group, or assembly of persons who teach, advocate, or encourage the overthrow or destruction of any such government by force or violence; or becomes or is a member of, or affiliates with, any such society, group, or assembly of persons, knowing the purposes thereof—
Shall be fined (up to $20,000) under this title or imprisoned not more than twenty years, or both, and shall be ineligible for employment by the United States or any department or agency thereof, for the five years next following his conviction."
It sounds to me like the FBI is following the applicable law. What you are advocating comes from the Declaration of Independence. It is not a law or part of the Constitution. Following your interpretation of what it says may make you a Revolutionary and admired by some. But it does not offer the protections offered by obeying the actual Constitution.