There's no such thing as hermaphroditism in humans; there's never been a single documented case of a human being capable of producing both sperm and egg.

In the medical literature, the term that used to be employed for some very rare types of DSDs was pseudohermaphroditism.

The term hermaphrodite comes from a story in ancient Greek mythology concerning Hermaphroditus, a son of the gods Hermes and Aphrodite who was remarkably handsome and very sexually attractive. The female adult nymph Salmacis fell in love with him when he was a youth, tried to seduce/molest him and was rebuffed. So Salmacis prayed to the gods to be forever united with the boy she lusted after. The gods granted her wish, and as a result, Hermaphroditus and Salmacis became joined in a single body, which was said to have the characteristics of both sexes. But if you look at ancient Greek statues and pictorial descriptions of Hermaphroditus, he always has breast buds (gynecomastia?) and very prominent male genitalia. Often, in fact, he has an erect penis of quit pronounced size.

People with DSDs, the doctors who study and treat them, and organizations advocating on their behalf have long asked the world not to use the term "hermaphrodite" coz it's not just wholly inaccurate, it's a stigmatizing slur that has been used to "other" people with DSDs for too long a time.

Sex is binary coz for sexual reproduction to occur two kinds of gametes are required: egg and sperm. And an egg and sperm are required each and very time, no exceptions. Human and mammalian reproduction can't occur, and never has occurred, with only one type of gamete.

Whilst there are wide variations in human sex characteristics - big dicks, micro penises; large breasts, tiny breasts; people who are very fertile and people who are infertile; men with low T compared to others of their sex, women with high T compared to others of their sex; etc - none of these variations changes the fact that there is/are no additional gametes beyond egg and sperm.

Similarly, in humans there are only two kinds of sex chromosomes - X and Y. In humans, there are no Q,R, S,T, U, V, W or Z sex chromosomes - just X and Y. And the key in determining sex is the presence of the SRY gene that's usually located on the Y chromosome. If an SRY gene is present and active, an embryo will almost always develop as male.

Most female humans are XX and most male humans are XY, but on occasion anomalies in sex chromosomes occur - resulting in conditions like X0 and XXY. But all these people are still clearly male or female.

On very rare occasions, an XX person is conceived with an SRY gene mislocated on one of the X chromosomes. Hence, XX males.

Also on rare occasion, XY humans with a functioning SRY gene on the Y chromosome have a condition that reduces or entirely eliminates their sensitivity to testosterone, so they develop in ways that cause them to appear to be female, and to be raised as such. But such people are infertile; they cannot create either egg or sperm, so they are not a third sex nor are they an "in between" sex.

Similarly, there are individuals with rare medical conditions that have "ovotesticular disorders" in which they have gonads containing both ovarian and testicular tissues. But most of these people are sterile, incapable of producing either egg or sperm. Those who can produce gametes usually can produce only ova, and it's not clear whether the ova is always or usually viable.

There are people with XX chromosomes with sperm.

Uh, no. People with "XX male syndrome" aka De la Chapelle, which usually comes about due to the SRY gene being mislocated on an X chromosome, are sterile - they produce neither sperm nor egg.

There are people with XY chromosomes with ovaries and can give birth.

Again, no. There have been a couple of cases of mosaicism, where most of the body has been found to have XY chromosomes but select reproductive organs have been found to have XX chromosomes.

Also, anyone who equates having ovaries with the ability to conceive, implant an embryo/get pregnant, grow a fetus and give birth is just showing their ignorance of the myriad female roles in human/mammalian reproduction.

In humans, the key organ in getting pregnant, gestating a fetus and giving birth is the uterus - not the ovaries. An XX female person can have healthy, fully functioning ovaries - but if she doesn't have a uterus due to a DSD like MRKH or coz she had to have her uterus surgically removed for medical reasons - she won't be able to get pregnant, grow a child or "give birth."

At the same time, an XY male person with a groin injury or a DSD like Caster Semenya's can be missing a penis, or have a penis so small or malformed that penetrative PIV sex is impossible - but if said person still has functioning testes, even if they are internal, chances are good he can father a child with medical assistance.