How can i get my boyfriend to realize that holding in anger isn't healthy?

Upbringing: A lot of times, men are "trained" from childhood to hold things in. Obviously this is not always healthy, but is kind of a part of our culture. Helping him to talk about it with you, and then possibly with a counselor might be a good start.

Dealing with anger: Holding in anger is often related to an underdevelopment in ability to use language to express emotions, and men tend to suffer from that more than women. You can help him learn how to talk about his feelings in a variety of ways, all of which require patience and caring to be successful. A resource is www.Gottman.Com, or taking a couple's communication class, or seeing a couple's therapist.