I am not the first to point out that bisexual individuals have traditionally faced discrimination even within gay and lesbian communities. While I'm not going to attempt to give a comprehensive explanation as to why here, I can think of a few possiblities. We're a species dedicated to classifying things, and then adding labels like "good" or "bad" to those categories.
Traditionally, whether it be a cultural or racial group, an exclusive club, etc. people tend to think "anyone in our group is "good" or "superior", while anyone in that other group is "bad" or "inferior". We stratify our society, based on these groups, with groups that are easily visually identified (race, gender) with whatever group that holds power (political/economic) and uses that power to place themselves at the top.
Any individual who breaks with societal classifications, creates a logic problem. "You're not in our group, therefore you're not good enough to be one of us." Bisexual individuals, by not having relationships with one gender and only one gender, break off from the gay/straight dichotomy.
Then there are those who lack a strong sexual desire to any sex. According to Wikipedia, "asexuality in its broadest sense, is the lack of sexual attraction... or the lack of interest in and desire for sex." In an over sexualized world, asexual individuals cannot be accused of following the norm.
Next up, there's the issue of transgender. Where sexual orientation deals with external attraction, gender identity refers to how one one identifies oneself internally. People who do not identify as either male/female can most broadly be classified as transgender.
The term transgender also encompasses a broad spectrum, including:
-Intersex - the condition where a person is born with indeterminate genitalia.
-Transvetism - used to describe a person who dresses up and assumes the mannerisms of the opposite gender.
-GenderQueer/Genderf*cks - Those who wish to flaunt the system entirely, usually will take on deliberately provocative styles of dress, usually incorporating both masculine and feminine features.
Of course this is just skimming the issue, but I also want to point out that in addition to the term bisexual, there are also labels for sexual orientations like pansexual and omnisexual which were created to acknowledge that there are more then two genders.
Getting back to the original point, transphobia is a very real issue. One could make the case that the bullying faced by gay and lesbian youth, is just as much about gender conformity as it is the result of homophobia. Boys and male teenagers who display weakness or effeminate traits, are the most likely of all to be bullied by their peers.
We believe in the absoluteness of good and evil so strongly we often forget to acknowledge the grey areas in between. Creating diversity is not about redeveloping superior/inferior paradigms, it's about believing that there is nothing wrong with being different.