I'm not saying that your friend wasn't taught this definition but from what I have read the official US definition is something to the effect of "Terrorism is the calculated use of violence or the threat of violence to attain religious or political ideological goals though intimidation, coercion or instilling fear." I think this is a fairly reasonable definition of terrorism. Unfortunately by this definition the US may well be the biggest terrorist state. Our invasion of Afghanistan might even be considered terrorism by this definition. We basically said, "Give us Osama or we will invade." (ie. the threat of violence to attain political goals through intimitadion.)
Not that this is really unusual. I expect that almost all governments engage or have engaged in terrorism of some type. What makes ours stand out is that we are large, have an enormous capacity dole out violence and are wealthy enough to support terrorist states all over the globe.