Overuse of antibiotics promotes antibiotic-resistant bacteria. Bacteria are designed to go into mutation mode when exposed to antibiotics. When a mutation occurs that cripples the metabolic pathway attacked by the antibiotic, the surviving bacterium transfers the mutation via plasmid to other bacteria. As long as the antibiotic is present, the mutants survive and the normal bacteria die. When the antibiotic is not present, the mutants, which are less fit to survive, die out.
You can get antibiotic-free beef at Earth Fare, Kroger, Trader Joe's, Whole Foods Market, and local farmers markets.