The phrase "a central justification of" is correct and usable in written English.
It can be used when discussing the main reason or rationale behind a particular argument, theory, or action.
Example: "The study provides a central justification of the need for policy reform in the education sector."
Alternatives: "a primary rationale for" or "a key reason for".
Any customs union makes it effectively impossible to negotiate free trade deals with other countries – one of the government's key ambitions and a central justification for leaving the EU.
That memo was used by the White House as a central justification for Comey's firing, but many law enforcement officials suspected that that was a pretext and that Rosenstein had been manipulated into providing cover for possible obstruction of justice.
As a central justification, it used pre-emption, or "anticipatory self-defense," which the White House defines as the right of the United States to attack a country that it thinks could attack it first.
Former CIA official Paul Pillar attacked the central justification of the current military escalation in an op-ed in the Washington Post last September, arguing that there was little reason to believe that a "safe haven" for Al Qaeda in Afghanistan would have any significant bearing on the terrorist threat to the United States.
Protection of human subjects This principle has been the central justification for the system of oversight of research in the US and in other countries.
This week the media are being correctly excoriated for their failure to be more skeptical of the Bush administration's central justification for the Iraq war: weapons of mass destruction that turned out not to exist.
The White House has been under intense pressure to start an investigation into why no one has found chemical, biological or nuclear weapons in Iraq when the administration made the immediate threat of such weapons the central justification for rushing this country into war without most of its important allies.
The two say the central justification for establishing a no-flight zone over Libya is that the rebels themselves are seeking military help to end the decades of Colonel Qaddafi's dictatorship.
