You can be angry without hate, but you cannot be hateful without anger. Anger is an emotion that refers to harboring extremely negative feelings toward someone, something, or everything. Anger is a strong emotion that leads to cruelty, violence, destroys peace, and may lead to hateful attitudes or pure, violent hate.
Hate is an emotion that has such disregard for someone, something, or a group of people that you may actually wish harm or death upon others. The existence and life of someone you hate means nothing to you. It is a state of being where you go from not caring to wishing ill upon a person.
Wars are founded on hate for another country or people. No one attacks a country because they are feeling a little sad or displeased. In war, a country is attacked because of anger that has led to hate for the entire people and government.
The word hate is thrown around liberally. When you say you hate an ice cream flavor, you do not literally hate the ice cream flavor and recipe. You are displeased and dislike it. Dislike and hate are two entirely different emotions. Disliking someone means exactly what it says; you don't have any fond attitudes toward that person at this point in time. To hate a person, however, requires such disregard for their existence, you would laugh at their death.
It is important to understand the difference between anger, disliking, and hate. You can be angry with your kids for misbehaving. You may slightly dislike your kids for a few minutes, but you do not truly dislike, much less hate your children. At a certain point in time you currently were not at a fondness level of 100% due to their behavior.
If your children are misbehaving and you say you hate them, then you have implied that you do not care for their existence out of unhindered anger. Parents who would dare to say they hate their children should in all honesty, not have kids.
The same goes for when a teenager "hates" his parents because he or she cannot go to a party or borrow the family car. The teenager obviously dislikes their parents at that point in time, but they do not hate their parents. Their anger at their parents is unloving, but it is not truly hate. The teenager does not literally want to harm their parents or wish them death.
Anger can be a temporary or long-term emotion. If anger consumes your personal being, then it turns to hate, and violent acts arise. Violence comes from a combination of extreme anger and hate. Hate leads to the downfall of the person who harbors too much anger as it builds up inside taking control of their life.