Eating the livestock (or drinking the milk) transfers antibiotics to our bodies, and then we become the environment in which bacteria are selected for resistance to antibiotics.
That's not how it works at all. The amount of antibiotics in slaughtered livestock is miniscule. In fact, the FDA requires a "clean out" phase for livestock treated with certain drugs to ensure the levels in the final meat are low enough.
Antibiotic resistance is generally spread via plasmid-mediated resistance. Overuse of antibiotics in any capacity, regardless of ingestion into humans, causes some bacteria to evolve resistance. Bacteria are promiscuous with their DNA, and resistance by one organism on one context (e.g. livestock) can easily get transmitted to a completely different organism in a completely context (e.g. humans).
Having said all of that, there are many potential antibiotics out there that haven't been fully researched (almost all currently prescribed antibiotics are beta lactam variants, which is only one small class), and this "cannot be treated" stuff is mostly just bad journalism.
Eating the livestock (or drinking the milk) transfers antibiotics to our bodies, and then we become the environment in which bacteria are selected for resistance to antibiotics.