Well, you could look at this two ways. Either they're trying to stop farmers as they claim from overmedicating their animals (unlikely, since Big Agra probably has staff veterinarians on call who will just write the scrips), or they're trying to close a loophole whereby people can obtain livestock antibiotics without a prescription, and use it on themselves. In other words, this could be just a way to eliminate DIY medicine and make people more dependent on the system.
Also, if you're a small farmer and you've been at it a while, you can probably diagnose many of the livestock illnesses yourself that might require antibiotics. So this is just burdensome and increases expenses and may even kill livestock during a delay as the farmer is made to wait for the vet to come out. There are probably only so many livestock vets to go around, and now they'll be working overtime.
Now I think sometimes people should go to the doctor, but if you just want antibiotics for just in case, like for a prepping stockpile, now it will be harder to get them. Better get them now before this dries up.