Fix things with my ex?

So I used to be in a relationship with this guy and it lasted 3 months. He decided to end it as he was studying abroad so we couldn't see each other and also because it has always been hard for him to be in a relationship, so he broke up before he'd cheat or something like that as he didn't wanna hurt me.

The thing is that he's back in town now for the whole summer and when we broke up, he suggested to be friends and I agreed but last Friday at a party i saw him kissing another girl and that kind of hurted me cause i still have feelings for him. He saw me crying and he grabbed my arm as he wanted to go outside and talk about it and he kept saying he still cares a lot about me and that i'm so important to him, that's why he doesn't want to lose me. He begged me to be friends again as he "stills wants me in his life" but i wasn't so sure so i told him i didn't believe him as I was really mad and he ended up leaving really frustrated.

I know i shouldn't have acted that way cause i didn't have any right at all to get mad at him if we are not in a relationship anymore, but what can I do to fix everything and keep in touch with him? I really don't want to lose him.
Fix things with my ex?
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