well it depends on what the fight is for. I just explained, terrorist exist. why wouldn't you want them exterminated? not sure what you feel is good about them existing.
As prior military and prior law enforcement, I have no good feeling about them existing. But, I do know we will NEVER eradicate terrorism, the best we can do is hold it at bay. Also, it is not the job of the US military to fight without letup in foreign nations. Do you honestly believe we should still be in Afghanistan? What goal are we trying to achieve that we have not achieved in the last 18 years?