We feed animals antibiotics because they live in confined conditions, literally in their own shit. Cows in particular need antibiotics because of their diet in concentrated feedlots. Said diet consits of corn mush, rendered fat from any source (including other cows and animals), and molases/urea mixture for protein. This diet is very acidic, while cows are ruminants with PH neutral stomachs. The acidic feed eats holes through the cows stomach, which gives it blood and liver infections. This is why cows are fed antibiotics. As for other animals, they recieve antibiotics because living in cramped conditions in their own feces is wholely foreign to them evolutionarily. Animals raised in more human/natural ways do not require any antibiotics.
Beyond that, non-organic animals eat grain with pestacide residue. This bio-accumulates in the animal, which once again bio-accumulates in us. Pestacides are a different issue and substance than anti-biotics. While organic animals are raised in confined conditions with grain feed (and are often fed anti-biotics because of it), they eat organic grain (which has no pestacide residue). Therefore, organic meat and dairy does not deliver the pestacide dose of its conventional cousin.
Also, green tea has been drank in large quantities for thousands of years, I wouldn't worry about it :D. I definitely agree about other supplements though. People need to be cognizant about what goes into their body...which brings me back to the pestacide/hormone/anti-biotic issue. The large concentrations of these substances in the american diet has not been analyzed by the FDA. Preliminary human and animal evidence gives me all the warning I need though.