I have farmed - successfully, with not a chemical anywhere, and a total "open door" policy to any farm visitors (to the total bemusement of the local NFU and min of ag types)
Should you actually take the time to do a bit of research into the field in which you claim expertise, you'll find that it is quite acceptable to use antibiotics on livestock in an organic farm, but unlike "conventional farming" the products from that animal have to be withdrawn for a suitable period to allow it's clearance from said animal, which is entirely reasonable, and ensures there's no chance of residues ending up inside the customers.
As for the subject of your unreasoned loathing - badgers..... without going all over old ground again - the ONLY way to ensure killing badgers is successful in preventing TB spread is to completely wipe them out - all the trials have shown that culls actually tend to spread the disease wider, and the only reason they're looking at a nationwide cull is as a sop to farmers who are somewhat hacked off at losing their stock to government policy
(note my choice of words - not losses to TB, but losses because of government policy!)
Let us for some ghastly acid flash moment assume you get your way, and the air is full of the scent of burning badger corpses, an entire species wiped out on the altar of ignorance - and cows continue to get/spread/have the disease spread to them by wildlife -what's next on your list of creatures to be sacrificed - deer, rabbits, hares, all birdlife?.............. there you are, standing in this silent chemicalised barren wasteland, hot 12-bore in hand with no income, because the general public have long ago lost any sympathy they had for you and your ilk....
If only for selfish reasons, widespread culls of wildlife are NOT the way forward, we need changes of policy, treatment of infected animals, and vaccinations of both cows and suspected wildlife vectors...........application of intelligence, not blind brute force and ignorance!