That's what you get for reading someones edits on Wikipedia.
By "absolute monogamy" Unwin meant a wife "under the dominion" of a husband who must be devoted to him for his whole life. He hoped that legal equality and strict chastity could be somehow reconciled.
He did not write that "equality" was "necessary" for absolute monogamy, since all known societies that had monogamy and chastity were highly unequal. With time, as they became more equal, greater sexualization followed and monogamy was lost. He speculated (he was not sure about it) that the inequality of society could be destabilising monogamy in the long run, and leading to people rebelling against it, as they pursue more equal relations and seek more equality, which in turn was accompanied by greater sexualization of society and the decline of monogamy, and then decline of society.
Unwin wrote that he hoped that implementing complete legal equality between men and women could make monogamy and chastity work without people rebelling against it, although he was not fully sure of that, as such equality never happened in history. But he never lived to see it. And we now have a confirmation that full legal equality does not lead to or sustain monogamy - it leads to massive sexualization of society and implosion of the family unit. In western societies, marriage is at an all time low while in many cases divorce and single motherhood is at an all time high.
His initial theory/observation is entirely confirmed. Initially, western societies were chaste, unequal and monogamous. They became rich and powerful, and demands for more equality followed. As western societies became more equal, sexualization followed and marriage declined. And today you have peak equality and in turn peak sexualization, zero chastity, and marriage levels at an all time low. His later speculation that implementing greater equality will help monogamy is thus rejected.
Now whats coming is that those societies will lose their power and will be replaced/destroyed, just as he found for many earlier ones.
1. Western societies are now declining and are projected to lose their power and to be economically replaced by Asia, which will account for most of the world's economy. The US is projected to bankrupt itself in the future. EU is projected to drop from 20 percent to 7 percent of the world economy, thus losing its power.
2. Modern, liberal white people have negative birth rate, which leads to their disappearance, and are projected to be replaced by more patriarchal brown and muslim people.
3. Things work in cycles and equality did not work. Phase 1 = Initial expansion (unequal, chaste society) --> Phase 2 wealth and power (somewhat equal society, people start to rebel against "old" customs) --> Phase 3 decadence (equal society, liberalism) --> Phase 4 decline (equal society is then conquered by more unequal society).