What would you say if your girlfriend says 'Promise me you're not gonna sleep with any other women'?

Anonymous
My boyfriend and I had a conversation about sexual relationship and he said 'guy sleeping with lesbian and woman sleeping with gay' doesn't really count as whatever.
So I asked him that 'will you be ok if i have sex with gay?' and 'well, it's not really counted' he said.
honestly i was shocked, to me, cheating is cheating and it doesn't matter if you cheat with gay or whatever'. he was meaning more like 'human is not monogamy from the first place', which I agree with on some level. But in my opinion, it's more about trust and how you control your emotional or sexual desire.
anyway, later, I said 'promise me you're not gonna have sex with other girls'. it was like me half 'tyring to break the ice' and half 'playing the baby'. And he got suddenly serious face and said ' I don't promise that I can't keep'. and that moment, I got even more surprised. not because i'm sad but because i started feeling uncomfortable with the fact that I'm in relationship with a guy who may pursue or sort of being ok with open relationship if there's no emotional attachment.
I mean, he is a great person. He doesn't seem a person who likes to have several girls at once. but if his view is totally different from mine in terms of 'what it means to be in a exclusive relationship' ,, well,, let's say there's a cheating in this relationship and what if he's like 'I'm OK with you because you had sex with a gay. I'm not mad at you' or ' i'm not even feeling sorry because I had sex with a lesbian, or just a girl without emotional attach' ? ... I am so confused.. I need some advice.
What would you say if your girlfriend says 'Promise me you're not gonna sleep with any other women'?
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