We took the kids to a ranch last weekend. We saw a bunch of sheep. Sheep have enormous testicles. I had been unaware of that. At first I thought it was ironic, considering how sheep are known for lacking courage while balls are associated with having it. Then I realized that "irony" doesn't begin to capture the sort of linguistic deception at work here.
Of course, idioms aside, balls are quite vulnerable, the sorts of things one would smartly do anything to protect. For example, desperate German shepherd fang avoidance. Off a cliff? Sure, just don't bite my balls.* The balls will control a sheep, or better, they will let a sheep be controlled. To be had by the balls seems a quite accurate idiom, with all it implies.
To have balls, then, is to be easily manipulated into supporting and/or doing things you don't actually want to do, like risking death to fight deeply hued people in the Middle East or working OT without pay;** to submit to leaders who'll have you running all over the fucking place because you're afraid of what they'll do if you stop running; to be always looking over your shoulder, behind, not ahead; to be enslaved, not free. To have balls is to be a...pussy? Sort of.
*I don't know how sheep would actually react to such a choice.
**I understand that sometimes the wolf is literally right on top of you and you gotta do what you gotta do...survival first, no shame in that...but that supports the point. John Steinbeck made this brilliantly clear in The Grapes of Wrath.