Based on the brain map model of transsexualism, being "agender" is technically impossible, while "bigenderism" may have some merit. Human fetuses are a blank slate in the womb, and during development, if biology so decrees it (i.e., if the sperm is carrying an X or Y chromosome), the fetus will be subjected to either estrogen (X) or testosterone (Y). According to this model, the brain of an FTM is masculinized in utero, while the body becomes feminized; likewise, the brain of an MTF is feminized, while the body is masculinized in utero. Why this happens, I haven't the slightest clue.
However, what I do know and can infer from this model is that, if one were to be truly agender, they would have no brain map - resulting in no brain. If the fetus does not come into contact with sexed hormones in the womb, they would not develop. Human beings are not designed to be genderless and anyone claiming to be "agender" is lying.
As for being "bigender", I have found it is easier to liken it to the intersex condition once known as "true hermaphroditism" (now known as ovo-testes), where an infant is born with both ovarian and testicular tissue. This is due to a mix up of chromosomes at fertilization where some cells contain 46 XX chromosomes while others contain 46 XY chromosomes. Seeing as the X and Y chromosomes determine which hormone the fetus is exposed to, a fetus could - very, very rarely - be exposed to both estrogen and testosterone in utero in which only the brain is affected and not the body. It is estimated that only 1-2% of the population is affected by a physical intersex condition, which would make this instance of "bigenderism" that leads to transsexualism even rarer than transsexualism itself (which occurs like, 0.3% of the time).
TL;DR: people who call themselves "agender" are calling themselves brainless, "bigenderism" could be a thing if you think about hypothetical biology really hard.