it is to america's benefit, and the world, to curb violence before it has an opportunity to expand.  We lost so many lives in WWII because we did not join the fight until they had already conquered most of our would be allies.  Had we stepped in as soon as they invaded poland, we would still have won, and lost far fewer lives.  

Also, we are in an international society now, american interests do not stop at our borders.  if extremist behavior spreads through the middle east and beyond, it would impact our domestic lifestyle.