The "War on Terror" is absurd because it's stateless and doesn't describe any one single group of people. It's a war on a very loose set of behaviors.
The average person thinks "War on Terror" and they support it because they have the people who brought down the Twin Towers in mind. Whereas people in the NSA, CIA, FBI, police stations across the country, etc, are thinking Occupy Wall Street, PETA, etc.
Social structures do things, and are amenable to institutional analysis. This allows us to act without omniscience. Institutional analysis allows one to analyze institutions independently of individuals; replace all the people, and you may nevertheless expect similar outcomes. Thus we can perform institutional analysis on governments, corporations, mafias, economies, consumers, managers, startups, etc.
If this weren't the case, humans wouldn't form institutions in the first place.
We Brits know this well, as we referred to the IRA terrorists, while many Americans and Irish called them freedom fighters, while funding them.
Perhaps consider this when Nelson Mandela dies. A man who for years was considered a terrorist, but is now almost universally considered a freedom fighter.
Note: I have mode no moral judgement about either the IRA or Nelson Mandela.
The falseness is this is in the application of morality labels. "Terrorist" implies something wrong and evil. Freedom Fighter implies nobility. Both are people using violence to achieve political aims. Much like the US does. Which means many world wide have every right to consider the US a terrorist state, since that terror is by a democratically elected government.
But yes, terrorism does mean something; just the way the word is used a lot, kinda doesn't... but this doesn't change what is terrorism and what is not. Even if someone where to argue that the ends justify the means, it would not change what those means are.