You ask why a person might want to reconcile with someone who has been abusive. The short answer is that the other might change. Forgiveness gives the other that second chance to actually alter a harmful pattern.
For those who want to examine the possibility of reconciliation, I recommend first asking yourself these three questions: 1) Does the one who hurt you show remorse, or an inner sorrow regarding what that person did to you? 2) Does the one who hurt your show repentance, or verbally apologizing to you? 3) Does the one who hurt you show any recompense or giving back to you in some way given that you are hurt?
These three (remorse, repentance, and recompense) are important for you to examine as you consider reconciling with the person. These three, if they are in place, will show you that the person has changed and so it may be safe to try reconciliation, at least in small steps, a little at a time until you are sure the other is trustworthy and will not abuse you.
For additional information, see Questions about Reconciliation.