Okay, let me start out by saying this is not an easy thing for me to say.
I was abusive in one of my past relationships. Up until that point, it was the only relationship that I ever truly took seriously. I thought I had met the man I was going to marry and that we would live happily ever after.
I grew up in an abusive home. Mostly mental and emotional abuse, which occurred daily, and weekly physical abuse that was so bad at times I had to stay home from school to avoid questions from teachers. I was terrified of my mother, the abuser, and angry at my father for not doing anything to stop her. I moved out when I was 17.
None of my abusive tendencies manifested themselves until I was 22 and entered my relationship with A. I never laid my hands on him, but I would throw belongings around our home, scream at him and call him names, and try to prevent him from seeing his friends and family because I was insecure. I was truly terrible to him and it is something that haunts me to this day.
He broke up with me after we had been together for 2 years. It was the roughest thing I have ever been through in my life, and it still is. It made me take a major fucking look at myself, though. I realized if I ever wanted to have a healthy relationship I needed to work through issues stemming from my abusive mother. I went to therapy. I confronted her, and my father and we worked through our issues together. Him breaking up with me forced me to look at myself and become healthy.
I am now in a new relationship. We have been together for 8 months, with no abusive episodes whatsoever. I now have the tools to effectively manage my emotions and explain my feelings.
I saw A last weekend. Even though we have been broken up for over a year and a half, seeing him is terrible and gut wrenching; not because I am still in love with him, because I know how badly I fucked up and how much I hurt him. I have discussed this issue with him many times, and the outcome is always the same: although he knows I am a changed person, we could never be together. He has the memories of me throwing shit around our home and screaming at him and terrifying him in his brain, and those will come rushing back to him if we were to give it a go. Everyone is different, and people do change, but once that damage is done it is generally irreparable. Leaving him and shutting him out is one of the best things you can do for him, because it will force him to take a long hard look at himself and change.
TL;DR: People do change, but once the damage in the relationship has occurred the memories will never be gone.