Do Antiwar Libertarians Hate the Military?

No.

What they do hate is the military's unnecessary, unconstitutional, and immoral acts of aggression.  Laurence Vance explains:

First and foremost is the claim that antiwar libertarians hate the military. I don’t recall ever writing anywhere that I hated the military. And neither do I remember reading where some other antiwar libertarian said that he hated the military. I hate many things that the military does, and think I have good reasons for doing so, as I mention below. I certainly don’t hate any individual members of the military or any other organization. I can’t speak for all antiwar libertarians, but here are some things I hate about the military:

• I hate the military fighting without a constitutional congressional declaration of war.
• I hate the military garrisoning the planet with bases.
• I hate the military targeting impressionable high school students (thanks to the NCLB act).
• I hate military recruiters lying to potential recruits.
• I hate the military fighting foreign wars.