If you found someone with whom you could be friends, would you demand that they abandon all their other friends, and became yours only, would you criticise them for talking to friends other than you, would you assume you could meet all their needs, and they could meet all yours? I'm going to guess not. Why, then, do we feel the need to treat relationships differently? The dominant paradigm in society is one of possessive monogamy, without even consideration of other kinds of relationship. Men who have sex with lots of women are studs, women who have sex with lots of men are sluts. In other words, it's acceptable for men to have a sex drive, it's acceptable for men to be possessive of lots of women, and in control, always having the choice. None of this is acceptable for women. Women are meant, both in the feudalistic, historic conditions of marriage, and in the norms of today's society, to be seen as possessions.
The institute of marriage contributes strongly to this sense of possession. Historically, men were expected to "worship" their wives, and wives "obey" their husbands. Although nowadays this has been removed from most wedding vows, the implication of complete and utter monogamy runs through them nonetheless, and hence through the institution. The idea, for most couples, when they marry, is to solidify some form of lifelong monogamy. For the majority of people, I think this is neither possible nor desirable. I don't deny that there are people out there for whom a completely monogamous relationship for the rest of their lives is necessary. One in every three marriages between 1995 and 2010 ended in divorce in the UK. In America, the General Social Survey indicates that 10% of married individuals cheat every year. Even the language around this is problematic - the concept of cheating implies that monogamy is the highest possible standard and that in some way it's like a game, on which you can cheat.
A lot of biphobia comes from this fear of cheating and the expectation that in a romantic relationship one party should meet all the emotional and sexual needs of the other. The fear of bisexual comes from the idea that they would require 'both' sets of genitals to be happy and have their needs fully met. If instead society didn't put this pressure on one partner to meet all the sexual needs of another, then this irrationality would be vastly lessened. For the record, as someone who is bisexual, I don't need to have 'both' sets of genitals on my partner(s) to be happy, and I don't think many bisexual people do, but this is about the perceptions coming from society.
My recent explorations of anarchism have caused me to question a lot of the social structures that we have in place. If I'm opposed to borders, to boundaries, to ownership, how can I justify upholding monogamy as the dominant paradigm, when that's about ownership and possessiveness. If I don't own or have the right to anything from anyone, how can I get jealous? I'm trying to explore this in my friendships and relationships at the moment - the idea that since I can't expect anything, I can't get jealous when people give things to other people.
I find it hard to imagine being happy in a non-monogamous relationship, but I think it'd make me happier than being in a monogamous relationship, with all the social pressure upon me and my partner to be the 'everything' to each other, to meet all of each other's needs, and the constant jealousy and fear that I'd be replaced by someone who does those things slightly better than me. In a non-monogamous relationship, I could learn to trust that I do everything I need to in my partner's life, that we love each other, and that everyone they love meets a different unique need. I don't know which type I'll end up in, but I know that, as a society, we need to break the idea that love equals perfect monogamy, familial love doesn't require that, friendship love doesn't require that, so why should romantic love?