The reason for this trope, in general, may partly arise from confusion surrounding the behavior of real life bisexuals, who do not, as a rule, date males and females simultaneously. In addition, most bisexuals prefer one sex over another at any one time and some will only occasionally date those who are the opposite of their stated sexual preference. They may even deny being bisexual if one were to directly ask them, and given the wide spectrum of human sexual behavior — and modern societal pressures — it would be difficult to tell a true bisexual from someone who's deliberately trying to hide their own sexual preference by dating members of the opposing sex. Furthermore, most people in general are monogamous, and will eventually settle down with someone (usually) of one sex or the other. This will lead people to conclude they were "never really straight" if it's with the same sex, or "never really gay" if it's with the opposite sex.
Even if bisexuals are admitted to exist and aren't simply liars (to themselves and everyone else), they are generally perceived negatively - either as depraved, greedy, or untrustworthy. After all, there's now twice as many people you need to worry about them cheating on you with. Generally, monogamous people expect total commitment from their partner, and there's the idea that this is impossible if your partner admits to having a whole facet of desire you will never be able to fulfill (for the opposite sex in a same-sex relationship, or for the same sex in an opposite-sex relationship).
To add to the confusion, there is a widespread assumption that one's sexual preferences must always line up with one's romantic preferences, which does not necessarily apply to bisexuals. A bisexual person may be sexually bisexual (as in, they are capable of being physically attracted to all genders) but they are romantically straight and thus only seek out romantic relationships with people of a different gender, or vice versa. This distinction, and the seeming disconnect between a bisexual person's physical needs and their romantic desires, can lead to the appearance that bisexuals "don't know what they want" or are just a "confused" straight or gay person.
Surprisingly, this trope is actually in effect within the LGBT community itself as well (despite the B standing for Bisexual). Many, many people initially come out as bi before identifying as homosexual. This has led to a widely held perception that, in most cases, bisexuals are just people who don't want to admit to themselves that they aren't really attracted to the opposite gender at all. This belief is probably compounded by the fact that a lot of bisexuals don't feel a need to hang out at LGBT events (and certainly don't need to move into a Gayborhood), so bi people tend to be underrepresented in the community anyway. There is also bona fide contempt (even hatred) for bisexuals from some corners of the LGBT community, who seem to think that bisexuals are "cheating" by liking both, that they need to "pick a side", that they're lying to themselves and everyone else (see above point), and/or that they "don't really count" as a member of the community anyway — which also contributes to bisexuals avoiding community spaces.
