SUBREDDIT: r/relationship_advice
TITLE: Is some kinds of cheating worse than others? My[21/f] boyfriend[24/m] asked another girl out on a date and told her that things weren't great with me.
POST: I have been dating this guy [24/m] for about 6 months but had been seeing him for a bit before that. He had always been super serious in the relationship from the beginning even though I had to deal with some personal doubts before I would begin the relationship. But after I began the relationship, I was in it for the long haul because generally he was good to me and we got along well.

At the beginning of May he asked a girl out on a date.

He had always called her his friend and she was taking courses with him so they had previously been around each other a lot. I am not the jealous type so never thought anything of it. In her response, she politely declined because she had just started seeing someone but also asked if he already had a Gf. He replied yes, but things were not going well. I only found out about all of this at the end of the month via a pop-up imessage on his macbook from his phone. 

I'm really looking for advice on how seriously I should be taking all of this. He and I are currently on a break after I confronted him about it. All he can say is he was drinking and feeling bad about the relationship. He says he doesn't have feelings for her, but how am i supposed to believe that? He has cried over it and assures me he has no more doubts. He technically did not do anything physically with another woman, but it really broke my trust with him. Am I taking it too seriously?
TL;DR: 
My Bf asked out another girl while we were dating? He's very apologetic and wants us to stay together. Is it a sign of future badness or should I give him another chance?