By far the most difficult concept to get right when it comes to intersex is the difference between sex and gender. This is one area that trips up many people (both gender conformists and non-conformists alike) and prevents them from "getting it."
Let me clear this up with a little Gender Studies 101: sex is biological, whether your gonads, chromosomes and genitals are male, female or intersexed. Gender, on the other hand is social, how other perceive you, and how you see yourself, masculine, or feminine, or, often somewhere in between, like a tomboy or a metrosexual. There is also considerable variation with interests such as a guy who likes to dance or a girl who likes cars, and it can also be situational, like a woman who takes charge when the pressure is on, or a guy who is secure enough with himself to cry. In spite of the incredible variation in gender, most people still see themselves as men or women, and most of society would agree with them (there are some people who consider themselves genderqueer, but they are few and far between).
There are many different ways to look at gender. It used to be "men are from mars and women are from Venus" They are so completely different that they aren't even from the same planet. The more common way now is to look at it as a spectrum. However I think this leaves a very big piece of the puzzle out. The piece is power. It is by domination that gender is defined. Even in a single sex group there is always a dominant leader, usually chosen subconsciously based on a myriad of social status factors(race, (dis)ability, wealth ect.) and personality. This leader is seen as more masculine, the alpha (fe)male.
Now you must be asking yourselves, what does all this have to do with intersex? Well intersex is a sex, not a gender, however there some obvious overlaps. For example most transexuals would be quick to point out that their brain structures resemble that of the sex they transitioned into, not the one they were born with. Also the more older brothers a man has, the greater the odds are that he will be gay. The theory behind this is because the more male babies a women has, the better her body will be at protecting itself from him and their cellular incompatibilities. In short he is bombarded with more female hormones in utero, feminizing him, resulting in a gay guy. These overlaps in gender and sex are especially important to intersexuals. We are no different then "normal" people, many see ourselves as male or female, just a little different then most. However, as I pointed out, there is an overlap with sex and gender, and many other intersexuals have a more complicated sense of their gender. In short, most of the medical abuse against intersexuals are out of fear that they will be "abnormal" or mistreated by others. This shows a remarkable ignorance to how varied gender is as well as strong latent homophobia and transphobia which, is not only wrong, but also stupid since many intersexuals lead mundane male or female lives.