(I’ve been asked this elsewhere and thought others might find it helpful.)
The modern use of the word “monosexual” was invented along with “bisexual” by European scientists in the late 19th century and early 20th century.
Back then, “bisexual” meant having a combination of male and female anatomical features, or a lack of sexual differentiation between male and female anatomy. “Monosexual” meant clear differentiation between male and female anatomical traits. Later, when bisexuality came to mean “having masculine and feminine psychological traits” (which is how Freud used it), “monosexuality” meant having the psychological traits of one “sex”. Under that framework, bisexuality also came to be understood as a form of attraction: it was presumed that people who had the anatomical sexual traits of “both sexes” also had “male and female” psychological traits, which meant that they also were attracted to “both sexes”. It was assumed that their “male side” desired females, while their “female side” desired males. Under this definition, “monosexual” meant someone with clear anatomical and psychological “male” or “female” traits, who is attracted to one “sex”. Note that they didn’t at all differentiate between sex, gender and sexuality. These were all considered as one and the same.They also used gender-binary language.
This term also had a particular value judgement: while bisexuality was firmly connected with immaturity, “primitiveness”, non-white/West-European (i.e. “savage”) cultures and with animals, monosexuality was strongly associated with maturity, advancement, “cultured” (i.e. West-European) humanity and whiteness. In this framework, monosexuality was clearly and explicitly superior.
Quite a bit later, in the 1990’s, the bisexual movements in the US and the UK used the word in a similar, but different context. Obviously, the meaning of bisexuality has changed considerably (it meant pretty much the same thing as it does now - referring only to desire rather than “anatomical sex” or “psychological gender”). Bi activists and writers used it to mean people attracted to no more than one gender, as part of a political dialogue about oppression. This is where I took it from and is pretty much how I use it. I will say that even then, the term was met with inner-community criticism, basically on the same grounds as now - that it created an unfair conflation between gay and straight people, and that it created a harmful binary dichotomy (bisexual/monosexual).
While I think that these criticisms have really good points, I also think we can take them into account, and use the term carefully, sensitively and contextually, without necessarily making those same mistakes. I think it’s one hell of a useful term for talking about structural oppression of bi people, so I guess you could say I use it tactically in order to raise those issues.