Not everyone who has an anger problem actually has a short fuse. It feels like they do at the moment. But once here in my office  we start talking more about it it frequently turns out that there are many other feelings underneath that anger. These feelings are often more difficult to talk about than getting angry.
These feelings tend to be sad, hurt painful feelings. Many people are not able to risk becoming so vulnerable as to express these feelings because they may not be well received.
It is so much easier to just get mad! Also, anger works! People who act angry generally get their way which then further reinforces the angry behavior.
​But it may be helpful to remember that asking the angry person about what might be going on with them and help them talk about the feelings under the anger, could open a whole new way of interaction, a whole new kind of relationship.