My girlfriend and I are open but she’s not comfortable with me having actual intimacy with other lovers (i.e. feelings, closeness) and she’d rather me have casual encounters vs ongoing affairs. I don’t want casual sex etc I want intimacy with my lover(s).. I’m not willing to compromise on my desiring deep relations with my lover. I’m someone who lusts for intimacy; I disdain superficial relationships. She cried so hard she almost vomited yesterday. How could we resolve this so I don’t hurt her?
It sounds like you two have needs that are fundamentally incompatible. You say you’re not willing to compromise, and also that this issue upsets her to the point of getting physically ill. There is no magic cure to resolve this without someone getting hurt or needing to compromise in an area they don’t want to.
Both you and your girlfriend are entitled to stick to your guns when insisting that you want certain things out of a relationship, but that may spell the end of the relationship. I am entitled to only date people who cook me breakfast every morning. If someone I want to date refuses to cook me breakfast every morning, then I can’t date that person. Or, I need to reconsider my no-compromise position. If I was in a relationship with someone who cooked me breakfast but suddenly stopped and refused to continue, we’d have to break up, or I’d have to compromise. There’s no having your cake (or breakfast, in this case) and eating it too.
It’s tempting to think that open communication can solve any problem - and to an extent, it does - but this sounds like a deeper problem than miscommunication. You may try talking with her about this, trying to find out why she is so upset about you being emotionally connected to your other partners, and maybe working from there to find a compromise - but honestly, if she gets so upset she gets sick when you discuss this, it doesn’t sound like a healthy conversation is possible. You need to decide which trumps: your desire for multiple emotionally invested relationships, or your desire to be in this one.