The Binary Genders are the two "primary" categories of genders used in a Western society. The opposite of binary is non-binary or abinary, which are umbrella terms including any genders that are not included in a binary gender system (this usually means genders that are not completely and solely male or completely and solely female). Binary gendered individuals can be cisgender or transgender. It's also a gender arity.
Exorgender is known to be a synonym of the gender binary.
Gender Arities in non-Western Societies
In Western society, the gender binary has two genders: fiaspec/women/girls/wifgender and miaspec/men/boys/wergender. However, not every culture or society shares this system. Some cultures may have more than two gender categories, such as certain Native American cultures. These are sometimes referred to as third genders.
Gender Binary in Society
Currently the gender binary is used to describe the misconception that men and women are the only two possible genders and that they can be assigned to them based on genitalia. This system often also typically enforces a masculine gender expression for men and feminine gender expression for women. This is almost directly a result of colonization causing the suppression of gender non-conforming, transgender, and non-binary, individuals as well as individuals with cultural gender binary identities. This system also tends to favor men, especially cisgender men.