It grants export subsidies to the processing industry, increasing reliance on cheaper industrially produced meat and dairy and encouraging dumping, which spells disaster for small farmers in developing countries, and it awards payments based on historical receipt of subsidies and historical production quotas (thus perpetuating the flaws in the system).
If major costs weren't hidden or externalized, the products of industrial farming would have to be priced a lot more highly, and there might then not be such a mass market for them. In fact, the whole concept of factory farming (i.e. maximizing output while minimizing costs) would become lame and therefore useless to the large corporations currently hogging the market.
In the meantime, people are buying two chickens for £5 in a Tesco's or ordering a "bargain bucket" in a KFC, feeling they're getting a good deal when what they're actually getting is poor-quality meat, three times more fat and a third less protein than 40 years ago, with an added dose of antibiotic residue and Campylobacter, that's costing them, and the rest of us, dearly. Let's face it, there's no such thing as cheap meat, milk or eggs; they're just a myth for naïve consumers.