It's about an emotional safety blanket. She knows you care for her deeply and that gives her emotional security: the knowledge that she CAN be loved and cared for.
Unfortunately, that's not enough for her. She wants to experiment, to be thrilled by meeting someone new and different, to have sex with someone else. You being her emotional safety blanket is WHY she feels secure in going out and meeting someone new. After all, if it doesn't work out, she knows you're still crazy about her.
See, this is the rub. She wants you to invest the same amount of emotional energy in her, as when you were sort of dating, now that she's officially dating someone else.
And this really comes down to how you feel about monogamy. Me, personally? My emotional energy goes towards my mate, the one and only. If we're not partners, you're automatically entitled to less of my emotional energy. It's a finite resource and to give it to someone who is simply a friend is basically, to me, ejecting half of your energy out into the void. Because it's not coming back to you, except in the friendship form. Relationships need equality. If you're sending out love, you need to be getting it back. Otherwise you're draining yourself and never refilling.
People in open relationships will likely disagree with this interpretation. Then again, emotional investment in open relationships tends to be lower because a) there's no exclusivity and b) there's multiple partners involved, each which takes their own little piece.
This is what I'd recommend. Learn to be her friend, not her lover, not her confidant, not her shoulder to cry on. That's a balanced relationship. Create boundaries, and be willing to say "Yeah, I don't know. You're going to have to deal with that yourself." If she can't tolerate losing your undivided support and sympathy and affection, then she made the wrong decision in deciding she needs to "see other people and sex and stuff." She sounds royally immature in that she doesn't see how unfair it is to you, to change the context of your relationship but expect the same level of emotional energy from you. That's bullshit. It's like your job firing you but asking you to come in on the weekends regardless.
So yeah. You've told her how you felt, told her what the consequences of her choices are in terms of your relationship....there's nothing left for you to do, except start rebuilding your sense of self, your confidence and put yourself back out there. It's brutal to go through but believe me when I say this a necessary part of EVERYONE's emotional maturity. From this you can learn what it means to value yourself as much as another person. For her....I guess she'll learn that the world isn't all about her needs and wants, that you can't take from people without giving back.
And yes, the withdrawal period from her will likely suck as bad as anything you've ever known. (Biochemically speaking, addiction to love can be like an addiction to a drug. Your body/mind gets used to one thing, then it's completely gone and you go into withdrawal.) It passes. What can help it pass faster is finding another woman who digs you. Because in the end, the agony you're experiencing is your ego, going "AAAAAHHHHH I'll never be happy/loved ever again!" Proving your ego wrong can help you get over your dependency to her....and nothing speeds that process along like a new fling. Assuming you can drag yourself out of your misery far enough that you're approachable, that is.