My girlfriend's not having sex, should I just break up with her?

She has PCOS and doesn't wanna be on birth control or use condoms because she doesn't like it and prefers the NuvaRing, which produces low dosages of estrogen in her cavity. So basically if I eat her out, I'm eating estrogen. HELL NO. She gives me her typical woman bull, "it's my body etc etc". Yeah well it's my body too and I'm not increasing my estrogen levels and growing shrunken balls and manboobs because the pill is too much of a inconvenience to you. My body produces enough estrogen for me, thank you very much. We haven't had sex because of this. Should I just break up with her? I mean what kind of guy would willingly risk shrinking his balls and growing manboobs because his GF is just a stubborn brat and it's a "inconvenience" to her?