The first thing that comes to mind is that behind that there’s a deep deep hurt.
We all get hurt and we react differently to getting hurt (i.e. get angry, get into a rage) but resentment is the type of emotion which is very hard, very deep, very long-lasting. Normally when we get hurt we go through the process of integrating what happened to us and if we completed it successfully - we are able to continue with our life and so to say “let go” of that hurt.
Resentment also can be there because there are “many hurts” accumulated - so the person was experiencing loads of separate cases of being hurt constantly over a long period of time. So it could be a build-up of unreleased and unprocessed emotions.
What makes it so hard for people to let go of it and to continue to hold on to it is:
Felling like if they are going to let go (i.e. forgive) it will mean that they are saying “it is OK to do that thing to me”. So by holding onto resentment they can hold on to feeling that they are always going to be reminded what happens and will not allow that happen to them again. It helps them to have a sense that they have boundaries. (Note: this is not the healthiest way to have the boundaries.)
They have identified with that feeling of resentment (victimhood) so much, that letting go of that would be letting go of their identity: they have been feeling this resentment for so long that they don’t know who they be without it. Some people get attached to the feelings and even though it is not good for them they don’t know anymore (cannot remember) who would they be without it. So they keep on holding on with it.
It may have become their life mission - it gives them purpose. If they have let go of this feeling, of this purpose - they would be lost.
So those are the things that come to mind first, there may be other reasons, but the bottom line is - in some way it is beneficial for them to keep hold onto resentment, otherwise they wouldn’t be doing that.
Having said all of that, even though resentment is not really healthy energy to hold on to - it does more harm to the person feeling it than the person/thing that this feeling is directed towards. However, often we cannot rush the process of letting go of resentment/forgiveness as ultimately the person has to decide for themselves when it is time to do it and then they can finally start releasing it.
Hope that helps.