There are many different reasons why someone may become a pescetarian, including health and ethical reasons. Because red-meats often contain a high amount of saturated fats, people often choose to cut meat out altogether. Additionally, studies have shown that pescetarians are at a significantly lower risk of heart disease compared to meat eaters [source].
Some pescetarians choose to eat only fish and seafood for ethical reasons. This may be because they believe that fish are not on the same moral level as other animals or because they feel that eating only fish is a good compromise between being a meat eater and a vegetarian.
Before I became pescetarian, I was a vegetarian for a number of years. As a fairly fussy eater, I found it quite difficult to get the necessary vitamins, minerals and protein to feel healthy. For me pescetarianism is a balance of the moral and ethical responsibility I feel towards animals and the planet, and my personal health and enjoyment of food.