Is it normal in relationships to say hurtful things?

I just want to know if this is a sign the relationship won’t work out or if it’s something people can move past from and have a healthy relationship. My boyfriend and I got into an argument and he said some very hurtful things. He said stuff like me not having many friends must reflect that I’m not a good person (I’m shy), how I think I’m such a perfect person (I know I’m not), that he chatted with another girl because he was annoyed with me, and that I don’t appreciate him enough (I try but I know I need to do better). I said things like “what’s wrong with you” and “you’re treating me badly, I don’t deserve this”. Some of the things he said were extremely hurtful and he did not apologize or seem to feel bad. I know I’m not the perfect girlfriend but I don’t think what I did warranted what he was saying to me. We’re taking a break right now so we can calm down and think but could a relationship even survive when so many insults were said? How could I learn to heal from this so we could move forward? I love him and I want to make it work and I want to be better.

Is it normal in relationships to say hurtful things?
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