Your ex exhibits a personality that you will find in many men. They don't want to be told they erred, they did a mistake, they hurt their significant other.
Your ex doesn't want to accept the truth he hurt you. He believes he has never hurt you. He is good. You are bad. He has never changed. You have changed.
You shouldn't apologize because you'll be strengthening his ego. There was a lady who asked for my advice pertaining to a problem that is similar to yours. She sent her boyfriend a text. She told him that he had hurt her because he didn't wish her a happy birthday. The next day, her boyfriend sent her a breakup text. That's a male ego which you shouldn't tolerate.
I suggest you don't contact your ex for a few days. This is to reduce the tension you feel and to enable you to reflect on your ex and the failed relationship.
After the few days of not contacting him, send him a text. Don't call him. Let him know how much you love him. Tell him that the mere mention of letting him know he hurt you, he dumps you instead of accepting it shows the kind of man he is. He doesn't want to accept the truth. Wish him well. Let him know you feel very hurt the fact he hurt you but doesn't want to admit it. Instead of accepting it, he dumps you which has increased the pain you're feeling. Thank him for everything. Let him know in time, you will heal from the hurt. You will recover and you'll have gained the strength to move on.
Think about it: can you live in a relationship whereby your man hurts you but doesn't want to accept that he hurts you? Will you be bottling up the continuous hurt in silence? That's not healthy. It shows a lack of respect.
If he calls you during the no contact, well and good. If he doesn't, don't beg. He has to accept the fact.
Forgive him. Let him know you've forgiven him. But you won't accept to apologize for something that you didn't do wrong.