Okay - yeah, the guy said virus rather than bacteria. Got it.
First of all, antibiotics, even when taken appropriately and in full dosage/cycle, do not wipe out all of, and only, the targeted bacteria. Certain classes of antibiotic work best against certain broad classes of of bacteria. Some (bactericidal) antibiotics directly kill bacteria, other (bacteriostatic) antibiotics only prevent the multiplication (growth) of the bacteria. No ingested or injected antibiotic is so specific that it ONLY effects the targeted strain or body system, and short of dosing to eradicate the beneficial "flora" in your body, most antibiotics destroy the bacteria to the point where your immune system can finish the job. Drugs targeted to UTIs, ear infections or respiratory infections will also kill beneficial bacteria in your gut. As a result, even following the most rigorous dosage of antibiotics, we remain covered with and full of bacteria, most of which (beneficial, benign and toxic) have now been exposed an antibiotic and the evolutionary selective process begins. This is obviously exacerbated with physicians prescribe antibiotics for viral infections. Even when it is a bacterial infection, without a sample/culture, it is only an experienced / educated guess at the specific strain, so often they prescribe more broad spectrum antibiotics.
You are right that the issue with antibiotics in cattle is the filthy, over crowded feedlot environment. A concentrated, high energy grain such as corn makes densely packed feedlots possible. Large feedlots would not be possible of cattle were fed prairie grasses.
Corn is massively subsidized in the US - in the form of direct payments, crop insurance subsidies, price supports, various counter cyclical programs and market loss assistance, which total anywhere from $3B to $10B annually. Approximately 40% of corn production is for animal feed. Corn is also fed to chickens (who exist in similar crowded, antibiotic infused environments) and "poultry litter" is then fed to feedlot cattle.
Corn subsidies -> cheap corn -> high energy, concentrated animal feed -> requires less (or no) pasture -> enables crowded feedlots -> increases spread of disease -> requires antibiotics.