So, my boyfriend and I have been seeing each other for about 10 months now, and around month 7, we decided to not be exclusive and to have experiences with other people (while also being with eachother). An open relationship. We discussed how we would be honest with eachother and tell eachother whenever had/ were going to have relations with someone else. We have done this. 
I happen to have Borderline Personality Disorder, which makes me get pretty irrationally upset about him having relations with others. But whenever it’s happened, I only get upset for about an hour, and he’s with me to calm me down and assure me he still loves me, and we are fine with that. 
This most recent time, he wanted to have sex with his best friend. I had a conversation with him prior about it, and told him that I would have an emotional reaction to it as per usual, but that I didn’t want that to stop him from doing what he wanted, and that we would get through it like we always do; and that I wanted him to have fun. 
So, time rolls around to when he’s supposed to be having sex with his friend, and we see eachother the day after. 
He straight up tells me, “we didn’t have sex”. So I ask, “did you do anything at all?” He says, “we cuddled”. 
I ask, “did you do anything else at all?” And he says no. 
I proceed to ask him why, as he seemed so eager to do it before, and he said “it just didn’t feel right”. 
As the night goes on while I’m with him, I sense that something is wrong and I know he’s hiding something from me, I just don’t know what. I tell him again, “are you sure nothing else happened?” He says no. 
And later on in the night I say to him, “you know, you don’t have to hide anything from me, I just want you to be honest with me and I’m not going to judge you”. He once again assures me that he’s not hiding anything and that he knows that. 
Later that night, I ask to stay with him as I normally would, and he asks me to go. Which is odd for him, so I leave; but continue to think he is hiding something. 
A few days go by; I go over to his house and get emotional because I think he’s hiding something. He gets frustrated with me, doesn’t understand why I’m crying, and begins to act aggressive. When I try to cuddle with him, he frustratedly tells me to stop and that he doesn’t want it. When I try to talk to him, he gets angry with me. When I leave, he slams the door. 
A week goes by, and we don’t see eachother. Until yesterday when he asked me to come over. 
He tells me that he left out something about the night that he saw his best friend, and tells me that he kissed him. 
I, obviously, get very upset that he lied to me 3 times about not doing anything and not hiding something. 
He says he lied because he didn’t want to cause an emotional response. 
But that doesn’t make sense to me because he already knew I would have an emotional response, but that we would get through it like we always do. 
I’m upset and hurt that he lied. 
I’m also upset and hurt because of the  conversation a few nights prior about him being honest with me, even if I’ll get upset. 
I feel like I can’t trust him ever again and I’m trying to figure out if me not being able to trust him is natural, or if it’s my BPD. 
I’m not sure if I should leave him, or give him a second chance. 

TL;DR: my boyfriend and I are in an open relationship, and yet he still lied about having relations with others. What do I do?