YEs, I am 100% certain. "Intersex" doesn't actually mean that they're in-between the sexes. They may have ambiguous genitalia, but each individual is still ONLY male or female. There is LITERALLY no alternative among humans - a single individual cannot produce both egg cells and sperm cells. It's not possible.
I'm not sure it's impossible
. Suffice it to say, that true hermaphroditism, where both types of sexual tissue are present, is quite rare. The successful production of both types of gametes has never been observed in such individuals, as far as I know.
Mmm... even in cases of true hermaphroditism, a person won't have two ovaries and two testes. They can't - ovaries and testes start out as the same tissue, and diverge during fetal development based on the chromosomal signals sent.
True hermaprhoditism is extremely rare - 0.0012%. Most commonly among that incredibly rare population are people who either have two ovotestes (a sterile tissue formation stalled halfway through differentiation) or they have one ovary and one ovotestis. These are female people (XX chromosomes, other internal reproductive organs are female) and they frequently have a malfunctioning SRY gene. This formation is somewhere around 3/4 of the cases. These female people are only fertile if they have one functioning ovary.
The remainder of the cases involve disorders that occur at conception: a single ovum ending up fertilized by two differently-sexed sperm, two ovum that fuse prior to being fertilized by a single male sperm, and vanishingly rare - two separate ovum, fertilized by two separate differently-sexed sperm that fuse after fertilization resulting in a true chimera.
In none of these cases will the individual produce both ova and sperm. In the majority of cases, they produce neither and are sterile. In no cases does a person have both a fully functional penis and a fully functional vagina. And in all cases, the person with the disorder is still only male or female.
One of the more common misunderstandings* is that "intersex" means the person is in between sexes, and thus that biological sex classifications in humans is a spectrum or is bimodally distributed rather than being binary. This occurs because people tend to conflate sexual characteristics with biological sex class.
As a reminder...
Biological sex class is based on gamete type, and is strictly binary. Disorders are possible that result in incompletely differentiated formation of the gametes, but they are vanishingly rare. In the very rare cases that it occurs, the person may have ambiguous external primary sexual characteristics, but don't have ambiguous internal primary sexual characteristics.
Primary sexual characteristics are based on reproductive anatomy, and are technically binary from before birth. This includes penis, testes, as deferens, and prostate in males. In females this includes ovaries, fallopian tubes, uterus, vaginal canal, and pelvic bone in females. These structures are binarily different in males and females in normal
formation. Medical disorders of sexual development can occur that interrupt or falsely trigger the sex-based differentiation process in utero in some very rare cases, resulting in external primary sexual characteristics that are ambiguous: formation of penis halted partway through development resulting in a structure that is either a very small penis (on a male) or a very large clitoris (on a female), or partial formation of scrotal sacks resulting in features that aren't standard formation labia or scrotum, or occasionally the urethral outlet doesn't transition into the penis and retains an secondary external opening near the base of the penis. Size and shape of these characteristics show variation among members of each sex, but there is no overlap between sexes, as the characteristics are sexually differentiated.
Secondary sexual characteristics are sex-linked features triggered by hormones that begin at puberty. These mark the transition from immature to sexually mature individuals. This includes the onset of menarche, growth of breasts, and widening of hips in females. In males, this includes the descent of the testes, elongation of the penis, growth of facial hair, virilization of the vocal chords and adams apple, and the accretion of dense muscle mass. These characteristics show considerable variation among members of each sex, but virtually no overlap between the sexes. Overlaps that do occur are invariably the result of a medical disorder, although not necessarily a DSD. For example, hirsutism in females isn't considered a DSD. It can result from a variety of conditions, including PCOS, adrenal tumors, and rare genetic disorders like congenital general hypertrichosis (I had to go look that one up
Tertiary sexual characteristics are sexually dimorphic features. These are features that vary between males and females, but are not directly tied to either biological sex class or to hormonal triggers. These tend to be evolutionary developments, and there's reason to believe that they are largely the result of sexual selection. This includes things like height difference, size of hands and feet, shape of eye socket, shape of jaw, etc. These are genetically determined and inherited, but there's a large variation within members of the same sex and considerable overlap between the sexes. For example, while it's generally true that males are taller than females, it's not rare to find a male who is shorter than an average female, nor to find a female that is taller than an average male.