Well, at the risk of sounding trite, it's complicated. It's a discussion with many layers.
At it's root, it asks the question: Is there any uncaused cause? Philosophers have been debating this for thousands of years with no clear answer, or at least one that can be proven.
On a similar plane, it introduces the question of whether we are no more than our genetics, our raised environment and exposure, our experiences in life, our mentors, education, etc... , and again, centuries of debate. For instance: Let's say a child is born in one country to a set of parents and extended family, grew up in a neighborhood in a certain area of the country, went to determined schools, and had a "normal" childhood, how would that young adult think, respond, and behave?
Now lets take the same fertilized embryo, implant it in the womb of a married mother in a different country, and all experience, education, and exposure to the world is totally different. The genetic combination is the same, but everything else is different. Would it end up being a different person with different behavior and personality. I think most would agree that the two different worlds would shape a very different person.
Back to the OP question. I think it is true, but it's not always true. I think it would be more accurate to say that hurt people can hurt people. Let's say a damaged person goes to the park every week, and happens to sit next to a retired therapist. They exchange a few words, and before long the therapist becomes aware of the hurt, and suggests they meet again in the tranquil setting.
After a year of doing so, and many conversations, the therapist helps the damaged person to see things in a different light and respond with different insights and is able to break with habit patterns. The injured has learned that everyone is fighting some sort of battles in life, and that understanding makes a difference. He may only be successful 50% of the time, but hopefully he is a work in progress that will get better with time.