
Question: In the scene where they cross the bridge with the train, and Allison French is being held by those two guys with a rope around her neck, so that if they would shoot the guys, the horse would run off and break her neck, suffocate her or whatever... They were with 4 against 2, so why didn't one of 'em just shoot that horse?
Answer: There's no explanation. It could be that no one thought of this. Also, even if they shot the horse, the girl could still be injured or killed. If the horse was only wounded, it could have bolted, reared up, or fallen and then rolled on top of the girl. There's many different scenarios that could have played out.
Answer: So they'd be unable to water their cattle. Which has two benefits for Fletcher. The first being that they'd have to take their cattle to the watering hole on the border of their property, making it easier for Fletcher to steal the cows. Second, and more long term, their cattle would be of poorer quality due to lack of proper care. The ranch would lose money as a result, and they'd be more amenable to selling the ranch to their competition, whom Fletcher works for.
Phixius ★