There are lots of reasons why you need to let go of resentment. Unless you are extremely lucky, most people have gone through some tough times in their life. When you look at the list of lemons that life can throw at you, some are definitely harder to move through than others. It would be fair to say feelings of anger and resentment are sometimes a natural result of being hurt. How you decide to react to poor treatment in life is important and can greatly impact your happiness.
There are many ways to look at this problem. Of course, there are many variables. Who hurt you? Why they did it? A common piece of advice that is often offered by professionals is "this too shall pass." The old saying "time heals all wounds" is often thrown around too. If it is about heartbreak you will often hear "it is better to have loved and lost than never to have loved at all." However, if a partner has just cheated on you and lied to you, it is hard to believe these sentiments at the time. This is when you need some reasons why you need to let go of resentment.
What can often happen is related to another cliched saying, "when one door closes, another opens." Of course, there are also the times when a seeming "curse turns out to be a blessing." If you think of times in your life where seemingly terrible things have occurred but you are then quite pleased with how things turned out, that is all great. You might look back on your time of pain and think, "what was I worried about?"
The one saying that people from Nelson Mandela to Lindy Chamberlain - people who were both jailed unjustly - have said is that if they continued to hold on to anger, the only person that would hurt would be themselves. This is a greatly evolved line of thinking. Most people have someone in their lives, who even in thought evokes the worst anger and resentment. It is important to let go of this. At the end of your life, you won't want to look back at angry feelings.
Ways of working through these feelings include meditations and affirmations. Try Louise Hay or Eckhart Tolle for inspiration on how to let go of painful memories. You will be doing this for you. There is a reason why forgiveness and letting go are so important; that is for your own peace of mind.