The extra fat contained in fried foods adds empty calories with little nutritional value.
Most people are overweight already and do not need more empty calories.
You really want to saute the chicken breast using as little olive oil as possible, and not dunk it in a pan full of hot oil. Use just enough oil to keep it from sticking. A very thin layer of oil coating the outside of the meat can help keep the meat from drying out during cooking.
The higher temperatures achieved in frying destroy vitamins and nutrients more than the lower temps common in other forms of cooking.
Many times foods are coated in a batter and then deep fat/oil fried. The batter adds extra calories, esp since it absorbs some of the fat and oil its being fried in. Again its extra calories with little nutritional value.
Foods are frequently fried in fats and oils other than olive oil, including lard. These other oils and fats are frequently saturated fats and trans fats(unhealthier than other fats) and contain things like cholesterol, which most people do not need to consume more of.