The Head of the Army and the Head of the Air Force might as well be interchangeable, based on how much they act the same. They’re the type of adults the BFG was talking about when he told Sophie, “Grown-up human beans is not famous for their kindnesses.” (15.15-19)
Aside from their lack of kindnesses, these people like being in charge and don’t like the unknown. They also don’t like the BFG because of his funny way of speaking. And they really don’t like travelling with him because he takes them off the maps on the atlas.
Apparently, lack of imagination and ultra-military mindsets go hand in hand. When they hear loud noises, they insist that the noises are gunshots. Even after the BFG assures them the noises aren’t guns, the Head of the Army says, “I am a military man and I know a gun when I hear one!” (21.93) He doesn’t think to ask the giant whether he knows giant snores when he hears them.
They also see nothing wrong with killing the giants, because the giants have killed so many humans. They’re the other side of the Queen and BFG’s two-wrongs-don’t-make-a-right argument. But they’re so over-the-top that their point of view gets swallowed up, making the Queen and BFG’s anti-killing attitude look all the better.