Perhaps every one of our top military, and several top civilian, people may be against it but there sure are a whole lot of other counties who believe that this is the best thing that could have ever happen for them, er, I mean, for us.
Fear monger much?
What percentage of our military budget goes to intervening in places where we should be keeping our nose out?
Hint: More than 12%
So you acknowledge the fact that the sequester will reduce our presence around the world. And the sequester will not give us much transition time. So we are just going to pack up and leave. You know what that creates? Instability. Whether or not we should be there in the first place is debatable but creating instability is not in our best interest.
As long as you have me going overboard with fear mongering let's just max out. Anytime any great empire falls the near term result is fighting amongst the regions that were once being held together by the overall presence of the larger power. The fall of the Soviet Union being the most resent, large scale, example. May seem a stretch too far but you acknowledge yourself we will be pulling out of regions around the world.
You're only looking at it from your point of view. Imagine some country that has always wanted to invade its neighbor. Before they might have thought, "Better not, even if the U.S. doesn't send troops they will at least help defend the other country." Now it will be, "If I invade my neighbor I get all their natural resources and worst case scenario my people will suffer under sanction while I load up my Swiss (no offense Swiss) bank account. U.S. still has it's bark but she lost her bite. The cat has left the building."