The basic reason for this is that diverting corn to ethanol production means that there is less corn to be made into animal feed. When this happens, the price of that corn goes up. When the price of corn goes up, the price of animal feed goes up. When the price of animal feed goes up, the price of the meat raised on that feed goes up. All of these price increases come about because of decreases in supply.
Supply is defined as the amount of a product that producers can and will sell at a given price. One of the things that makes supply decrease is when the producers have an alternative use for the product. That is what is happening with the corn for animal feed. When corn is diverted to ethanol, the supply of corn for animal feed goes down. When supply goes down (all else being equal) price goes up. So, the price of corn for animal feed rises.
Another thing that causes supply to decrease is an increase in the cost of inputs. Corn is an input of animal feed. Therefore, if the price of corn for animal feed rises, the supply of animal feed drops and its price rises. Animal feed is an input for meat. When the price of animal feed rises, the supply of meat falls and its price increases.
Through these steps, an increase in production of corn ethanol raises the price of meat.