There are only 2 genders

cdog1950

@Fredsnephew ;

Hypothesis: "There are only two genders."

1).
From Wikipedia

In biology, a hermaphrodite is an organism that has complete or partial reproductive organs and produces gametes normally associated with both male and female sexes.[1] Many taxonomic groups of animals (mostly invertebrates) do not have separate sexes.[2] In these groups, hermaphroditism is a normal condition, enabling a form of sexual reproduction in which either partner can act as the "female" or "male". For example, the great majority of tunicates, pulmonate snails, opisthobranch snails and slugs are hermaphrodites. Hermaphroditism is also found in some fish species and to a lesser degree in other vertebrates. Most plants are also hermaphrodites.

Historically, the term hermaphrodite has also been used to describe ambiguous genitalia and gonadal mosaicism in individuals of gonochoristic species, especially human beings. The word intersex has come into preferred usage for humans, since the word hermaphrodite is considered to be misleading and stigmatizing,[3][4] as well as "scientifically specious and clinically problematic".[5]

A rough estimate of the number of hermaphroditic animal species is 65,000.[6] Since the estimated total number of animal species is 8.6 million, the percentage of animal species that are hermaphroditic is about 0.7%. Arthropods are the phylum with the largest number of species. Most hermaphroditic species exhibit some degree of self-fertilization. The distribution of self-fertilization rates among animals is similar to that of plants, suggesting that similar processes are operating to direct the evolution of selfing in animals and plants.[6

Protandry: Where an organism is born as a male, and then changes sex to a female.[12]

• Example: The clownfish (genus Amphiprion) are colorful reef fish found living in symbiosis with sea anemones. Generally one anemone contains a 'harem', consisting of a large female, a smaller reproductive male, and even smaller non-reproductive males. If the female is removed, the reproductive male will change sex and the largest of the non-reproductive males will mature and become reproductive. It has been shown that fishing pressure can change when the switch from male to female occurs, since fishermen usually prefer to catch the larger fish. The populations are generally changing sex at a smaller size, due to natural selection.

Protogyny: Where the organism is born as a female, and then changes sex to a male.[12]

• Example: wrasses (Family Labridae) are a group of reef fish in which protogyny is common. Wrasses also have an uncommon life history strategy, which is termed diandry (literally, two males). In these species, two male morphs exists: an initial phase male and a terminal phase male. Initial phase males do not look like males and spawn in groups with other females. They are not territorial. They are, perhaps, female mimics (which is why they are found swimming in group with other females). Terminal phase males are territorial and have a distinctively bright coloration. Individuals are born as males or females, but if they are born males, they are not born as terminal phase males. Females and initial phase males can become terminal phase males. Usually, the most dominant female or initial phase male replaces any terminal phase male when those males die or abandon the group.

Bidirectional Sex Changers: where an organism has female and male reproductive organs, but act as either female or male during different stages in life.[12]

Clearly in the natural world there are more than two genders, with the minimum being three, but I would say five or six is more likely.

2).

Also, homosexuality cannot "infer" anything.

(verb (used with object), inferred, inferring. 1. to derive by reasoning; conclude or judge from premises or evidence:)

I believe you mean that the existence of homosexuality does not imply a separate gender.  No, it does not, but it may demonstrate the degree of uncertainty in trying to confine the range of human consciousness to your two boxes.

3).

gen·der

/ˈjendər/

noun

• 1. the state of being male or female (typically used with reference to social and cultural differences rather than biological ones)

As I noted previously, in humans, what we describe as maleness is primarily the result of the expression of the SRY gene on the "Y" chromosome.
From Wikipedia,

"Embryos are gonadally identical, regardless of genetic sex, until a certain point in development when the testis-determining factor causes male sex organs to develop. Therefore, SRY plays an important role in sex determination. A typical male karyotype is XY. Individuals who inherit a normal Y chromosome and multiple X chromosomes are generally male (such as in Klinefelter Syndrome, which has an XXY karyotype). Atypical genetic recombination during crossover when a sperm cell is developing can result in karyotypes that do not match their phenotypic expression.

While the presence or absence of SRY has generally determined whether or not testis development occurs, it has been suggested that there are other factors that affect the functionality of SRY.[17] Therefore, there are individuals who have the SRY gene, but still develop as females, either because the gene itself is defective or mutated, or because one of the contributing factors is defective.[18] This can happen in individuals exhibiting a XY, XXY, or XX SRY-positive karyotype.

Nevertheless, even the sex-dichotomous differences are not absolute in the human population, and there are individuals who are exceptions (e.g., XY males with a uterus; undeveloped testes), or phenotypical females with an XY karyotype (undeveloped reproductive organs), or who exhibit biological and/or behavioral characteristics of both sexes.

Sex differences may be induced by specific genes, by hormones, by anatomy, or by social learning. Some of the differences are entirely physical (e.g., presence of a uterus) and some differences are just as obviously purely a matter of social learning and custom (e.g., relative hair length). Many differences, though, such as gender identity, appear to be influenced by both biological and social factors ("nature" and "nurture")."

This subject is too complex to be put in an "either-or" box. Given the above, it is clear that humans also have more than two gender possibilities, if for no other reason than that until the 6-8th  week of development all humans are either/or sex.

Consequently, in the natural world (in which we are included) your hypothesis is totally invalid. 

Fredsnephew

@cdog1950 ;

What are we discussing here?

Are we discussing gender issues relative to the human species?

Or are we discussing a broader subject?

cdog1950

Well the question posed was are there only two genders. Not are there only two human genders (as I understood it).  But honestly, as a trained biologist I have never really delved into the subject. Once I got started I came to believe that we have failed (as scientists) to really addressed the issue.  We tend to anthropomorphize the natural world into the two most evident sexes that we see in ourselves.