sorry, i am going to disagree
i have chased mine away on occassion because they were doing bad/dangerous things .... they are not fearful and what i am doing is not characterized as "beating" ... same as spanking a child is not characterized as "beating"
i can tell you with certainty that a slap to the neck is a lot softer than a horse bite or a horse kick .... and they do that to each other all the time
There is a difference between "chasing" as in taking a few quick strides forward and driving them off, and "chasing" as in literally running at them with a whip. I wrote the whole comment entirely out of experience. My mare actually became aggressive towards the lunge whip because of misuse of it. I'm not exactly sure how it got started, as I never ran at her with a lunge whip. She still is aggressive towards it on occasion, but is much better than before.
I have no problem with giving a horse a swat or a slap to the neck. However in this situation the mare was going forward
into DD's space, so she needs to be forced to move backward
out of DD's space. By slapping her on the neck in this situation, it is teaching her that it is ok to walk ahead of the handler as long as she is not right next to them. The horse should always be at the shoulder, and not in your space bubble. It's the principle "always do the opposite of what the horse wants to do", though whether I follow that principle depends on the situation. In this situation, yes definitely. It is the same idea as when you ask a horse to go right, and he goes left. Do you correct him by forcing him to go right or left then? If you force him to go left, even if he's getting turned in tight circles and getting kicked in the side, he's still won. He got to go the way that he wanted to. But if you force him to go right, you are reinforcing your command to go right, and reaffirming your position as the dominant lead horse.
All the advice I've given comes from my own experience, not theory or something I've read. I have learned first hand what works and does not work.
Something I learned the other day-I read a post on here that if you are in a pasture and you want the horses to get out of your space, take a lead rope and swing it behind your butt as if you are a mare giving a warning to get away or she will kick. I tried this the other day with my horses. They were crowding me at the gate, so first I lightly swung the rope while facing them. They backed off a little bit, but not much. Then when I got inside the turn out, I turned around and swung the rope behind me. You would not BELIEVE how fast they took off! They were practically stumbling over their own feet until they were fifteen feet away. This was the sequence of my expressions:
See? No chasing or whipping required. Just a pretend mares tail.