1. Criticisms leveled against Consequentialism.
Consequentialism is based on the consequences of actions. It is sometimes called a teleological theory, from the Greek word telos, meaning goal. According to consequentialism, actions are right or wrong depending on whether their consequences further the goal. The goal (or, "the good") can be something like the happiness of all people or the spreading of peace and safety. Anything which contributes to that goal is right and anything which does not is wrong. Actions are thought to have no moral value in themselves (no rightness or wrongness), but only get moral value from whether or not they lead to the goal. John Stuart Mill was a famous consequentialist. Consequentialists would say that killing people is not right or wrong in itself, it depends on the outcome. Killing an innocent child would be a bad thing because it would decrease the happiness of its family and have no good results. Killing a terrorist would be a good thing because, although it would upset his family, it would make people safer.
The main criticism of consequentialism is that it would allow any action in pursuit of a good cause, even actions that most people would say were clearly morally wrong, such as torture, killing children, genocide, etc.
2. Criticisms leveled against Deontology
The word deontology comes from the Greek word deon, meaning duty. According to this theory, it is your duty to do actions which are right and not do those which are wrong. Actions are thought to be right or wrong in themselves. For example, killing people and lying are wrong, sharing with others who are in need is right. Immanuel Kant was a famous deontologist.
E.g. While trekking in the Andes you come across a guerilla leader who has captured 20 local villagers. The guerilla says if you will shoot one hostage he will let the other 19 go free. If you refuse to shoot, he will kill all 20. In the...