Females always know that they are the mothers of their children. Males depend on trusting the female on being the father. (This is before DNA testing was available, but even DNA testing isn't perfect, is expensive in most countries and is not normally used unless there are suspicions of genetic conditions or a legal conflict).
Since reproduction is about passing on your genes, then males have an incentive to make as sure as possible that females are exclusive to them. Females don't have an incentive to have their males be exclusive; only to have them reliably provide for them and their children.
That has nothing to do with sexual desire in itself. I'm convinced by what I've seen that females have a stronger sex drive than males, on average.
This is why my preferred theory for the aetiology of GL, among competing ones, is that adult males make sure that a female will be with them since before she is fertile. Of course this would not apply to same sex CL or to Fb CL.