My boyfriend (23M) cussed me out (23F). Do I continue with him?

So I (23 F) was out with my boyfriend (23 M), we are 3.5 years together, and everything was well until we went on coffee date. When we sat, I was telling him about agenda and he asked to show him the agenda and cuz his phone was closes I told him to give me his phone so I’ll show him. He started complaining why don’t I look on my phone and why my phone is in my bag mostly. He started accusing me of cheating when I touched my phone, right after he picked up his while we were mad at each other. We didn’t talk much after.

Then he picked up the bill and took me home with his car. We were still mad and while he was driving he told me to either be loyal and stand like a true woman next to him otherwise I’ll have problems. I told to him to first be a real and true man if he wants a true woman next to him. He got so mad, he brake the car and threw his hat nervously in the back of the seat, said he will drop me off car but continued anyway and sped up very fast and started yelling and cussing at me who am I to take down his masculinity, how dare I told that to him, he called me trash and said ‘I’ll f u everything, f u this and that, I’ll show u now who is real man’, he yelled at me to shut up. After, he pulled up calm down and said sorry, I did too. But I swore in front of him to God that I won’t continue with him no more cuz this happened before too and it was a boundary and he promised not to break it but he did anyway, and said I provoked him. Later he was trying to convince me to stay with him, still yelled and was hitting the steering wheel cuz I wanted to leave him. He didn’t want to drop me home, he wanted me to tell him that everything will be fine and we will continue in the relationship together.

Today he called me couple times, said sorry and was very calm on phone and wanted to go out with me to solve this issue saying that I mean a lot to him and that I am everything to him and his happiness. Even tho I was mad and told him there isn’t a chance for us he kept begging and won’t leave me, he is persistent and never lets me leave the relationship. He gave me a rose today that was very beautifully decorated with a romantic card for apology, saying how sorry he is for his reaction and that it won’t happen again, that he feels peaceful with me and will do everything to keep me in his life saying I mean a lot to him.

I’m not sure whether I should continue with him. This is third time he reacts like this, cussing and yelling. Previous time he promised he will change. I am so confused. I’m not sure whether is it worth staying, what is this behaviour and why does he do it. I suspect he is a narcissist and abusive.

TL;DR;: My boyfriend cussed me out and yelled at me