More like the phrase comes from observed behavioral patterns in reproduction habits of women stemming from biological evolution. The more they can back-stab each other and drag the others down, the higher the chance of getting a higher value male.

Women don't have the testosterone fueled violent tendencies of males to get into physical competition to assert dominance over sexual competitors, so they resort to more subtle and cunning ways of "thinning the herd" of sexual competitors.

or "misery loves company"