Isn't the reason obvious?
If President Trump, the Pentagon, and the CIA succeed in instigating a war with North Korea, guess who is going to pay the biggest price for such a war.
No, not the United States. At the end of such a war, the continental United States will remain untouched, just like it was after World War I, World War II, the Korean War, the Vietnam War, and all the other foreign wars in which the U.S. government has become embroiled.
The same cannot be said about South Korea and Japan. While North Korea would undoubtedly end up losing a war against the United States (assuming that China doesn't enter the fray), South Korea will end up as a devastated wasteland. That's because as it is going down to defeat, North Korea can be expected to cause as much death and destruction as it can.