The thing about intersex is that it's about as far from a black and white issue as one can really get.
In general, the only intersex conditions that people really think of when they hear 'intersex' are babies with 'ambiguous genitalia'. Many take this to mean genitalia somewhere between a penis and a vulva, but it's not so simple, and is often subject to the biases of society. Cases of micropenis have often seen the babies reassigned as female, with the micropenis becoming a clitoris. Conversely, cases of a considerably larger than normal clitoris but otherwise 'normal' genitalia has led to children having the clitoris amputated *shivers*.
But then there are other intersex conditions to consider, in particular the nature of chromosomes. A cis male can have XX chromosomes, and a cis female XY chromosomes, and they can go for decades without ever knowing! In general, those with the condition often only find out because of the infertility it causes.
And even then there are so many other conditions to think about, and where the line should even be drawn regarding what is 'intersex' and what is 'dyadic'. For instance, take a cis male who has normative genitalia and XY chromosomes, but a larger than normal amount of estrogen, leading to secondary sex characteristics which are traditionally considered 'female' - by medical standards, he wouldn't be considered intersex, even though his 'sex' is evidently different from what is 'expected' of cis males.
The simple truth of the matter is that nature doesn't cut and paste people into 'male' and 'female' categories as readily as most people presume. Rather, there is considerable variation, and it is the pressures of society that lead to the medical establishment assigning genders based on how the person's body looks.
Somewhat related personal side-note: when I researched intersex conditions a few months back, I saw some information on those assigned male who have two X chromosomes, and I thought that I had a lot of the symptoms. However, as it turned out, my mother had to have my chromosomes tested while she was pregnant with me (she was over 40, so they wanted to test for Down's syndrome) - turns out I have the standard XY. At the time I thought "Damn, that would have explained so much..."