Okay. I see the last bit has been addressed. Moving very swiftly on. The reason I'd argue that you do need to buy what I am selling is because of what you originally said wasn't fair.
Firstly, it's important to understand that your mindset about this isn't anything new to most of us. Most of us have heard every single reason why people feel they must have gender based restrictions and seen where and why they work out over the long term for only a minority of people.
With your case, I'm guessing that your partner doesn't want you to date women for pretty much the same reasons you don't want her to date men: Fear of replacement. You feel that another man would naturally threaten your positon as her man in ways that a woman would not. She feels the same about other women. The thing is, she is bi and you are not. So that leaves her with the option of dating women and you the option of learning to be attracted to men to achieve some sort of equality in an open relationship. You said you don't feel this is fair. You can't help that you aren't bi.
That's why I am suggesting that the way forward is to both accept that a gender based restriction will not protect your relationship. Monogamy won't even guarantee that neither of you will fall out of the love with the other or in love with someone else. If you can both work on developing a different mindset, it will allow you both the freedom to date who you are attracted to rather than creating an unequal situation where you are forced to accept a One sided open relationship due to your sexuality.
You might be interested to know that I have known of bisexual people in heterosexual relationships who have tricked their partner into doing emotional labour that they were not prepared to do by encouraging them to pursue these lines of thought. What they ended up with is a monogamous partner taking care of the house and family duties while they got to have fun and sexy nights with other people of the same sex. Some of those would become deeply entangled relationships. I'd make sure that isn't happening to you.
Nope, still not buying.
It will not be onesided as I can have casual sex with women, quite possibly with a friend of hers. She lives almost next door so I guess there is a chance that every time my gf goes on a date I will be getting some attention to myself. If not, it is not that big of a deal.