Your way of life got destroyed by a guy in a cave half the world away, and then a dictator of a small country finished the job with some propaganda and some cash to grease the right palms. A response can be quite effective even if it isn't by men in uniform.
It's not "my" way of life. I'm not american. I'm just saying that it's a basic geopolitical fact that anyone who's actually foolish enough to declare war on the USA is going to get killed.
Military response means men in uniform battling for their country. Terrorism is not a military response, it's one of several ways to cope with the enemy's superior military forces. They can't overtly bomb america back to the stone age, so they resort to tradecraft and clandestine operations.
It actually works, which is why governments pull all the stops when it comes to fighting terrorists. Even this plays into their ideological objective of forcing america to compromise on its founding principles, thereby corrupting it from within.