Complementarianism

Complementarianism, closely related to the Separate Spheres ideology, is the view held by various religious groups that men and women have different, complementary roles (generally "headship" roles for men, and supportive roles for women) in various walks of life, including family life, social interaction, and religious rites and practice. Complementarianists hold that, although men and women evolved/were created equally, they evolved/were created for different (yet equal!) purposes. It is usually religiously based; however in theory secular complementarianism could, and probably does exist. It's basically doublespeak for sexism, religiously motivated or not.

Though when worded carefully, complementarianism doesn't sound sexist, it almost always leads to a less-than-egalitarian society, such as American society up until the rise of feminism in the mid to late 20th century. Upon closer examination, complementarianism is, at the end of the day, fancy-looking sexism. Since women are generally given the "supportive" roles in life, this means that they're generally confined to the home, and encouraged to make life as comfortable for the man as possible, while he acts as the "head" of the household. This can, and did, lead to non-suffrage for women, and women not having the ability to obtain divorces, the latter seen today in some Orthodox sects of Judaism.

Christianity
Many, many, Christian sects and denominations endorse some form of complementarianism or the other, including several Protestant denominations, the Roman Catholic Church, and the Eastern Orthodox Church. Christian complementarianists hold that "God has created men and women equal in their essential dignity and human personhood, but different and complementary in function with male headship in the home and in the Church." is commonly cited as evidence for Biblical complementarianism: "Wives, submit yourselves unto your own husbands, as unto the Lord."

Islam
Two main streams exist in Islam that are equally prevalent in both Shi'a and Sunni, the egalitarian stream and the complementarianist. The Middle East is a prime example of complementarianism in action, with women being disadvantaged widely throughout the Middle East, such as the widely known ban on women driving in Saudi Arabia, which is defended on the basis that letting women outside of the home to drive cars would "expose them to evil", like it doesn't do for men.

Judaism
Complementarianism is the least apparent in Judaism among the Abrahamic religions, existing where it does in the stricter, more fundamentalist Orthodox sects. Generally, in Orthodox Judaism and sometimes Conservative/Masorti Judaism, women aren't permitted and sometimes even outright discouraged from becoming cantors or rabbis, while Reform and Reconstructionist Judaism actively encourages female rabbis and cantors.

Other versions
Gevorg Geodakyan offered an evolutionary theory that claimed sexual reproduction with two genders (rather than hermaphrodites exchanging genes) arose to allow different genetic functions for the two sexes: women exist to conserve genetic material and provide stability in the gene pool, while men are experimental vessels where all kind of weird shit will happen; this supposedly corresponds to the idea that women stay home and do nothing and are sensible, while men (with their greater variety of genes making some geniuses at different things and others comprehensively idiots beyond all female stupidity) go out and do wild and amazing things in the world at large.