The hormones ARE what make it biological (among other things, but hormones are one of the most important factors). The testosterone and estrogen you're exposed in utero to play a substantial part in determining how one identifies. More testosterone, and you're more likely (key phrase: more likely; not necessarily a guarantee, to my knowledge) to identify as a guy. More estrogen, you're more likely to identify as a female.
@o Ventus this isn't targeted at you. It just seemed a good place to insert it.
I explained the mechanics of this a while back. To quote myself:
Re: What makes a Trans person feel the way that they do: (current scientific hypothesis; TLDR version)
All humans embryos start out as biologially female. At ~ 8 weeks, a series of hormonal washes - dependant primarily on your chromosonal composition, e.g., XX, XY, XXX, XXY, XXXX, XXYY, XXYYY, Mosaic, etc, but also some other factors - trigger changes throughout the body (including the brain). If these hormonal washes do not proceed in exactly a certain way in certain amounts at a certain time, the embryo will not be definitively XX - hetero female, or XY - hetero male. Generally, it's "close enough", but not always. Since these changes are body-wide, they also effect brain development, and thus self-awareness and thought. This can lead to, for example, possessing "male" genitalia with a "female" brain, among a wide variety of states. It's not a mistake or error. It is perhaps uncommon, but still perfectly within the expected parameters of human development, much like having a particular combination of hue, shade, tint and tone makes your exact skin, hair or eye color.
This is a vast, vast, over-simplification just for the sake of helping you begin to understand the basic mechanisms behind "why".
Sex and Gender are biological. Gender roles and the assumptions people make about them are societal.