“I know you belong to somebody new, but tonight you belong to me.” Rose and David
“I wanted love, I needed love. Most of all, most of all.” Auerbach and Carney (1)
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Several researchers have attempted to reconstruct the very difficult problem of why pairbonding may have evolved in humans (I wrote about this here, but a decent guess is that this began around 2 million years ago. Maybe). Those reconstructions often come with an addendum, which predict that pair-bonds would not be completely symmetrical. Instead, either males or females would have more of an incentive to initiate or maintain a long-term bond, and this would depend on the reasons that pairbonding evolved in the first place.
For example, here is David Buss, explaining why males are more likely to fall in love first:
“Because love is an emotion tethered to long-term mating; because fecundity and reproductive value is so critical to men in selecting a long-term mate; and because physical appearance provides an abundance of cues to a woman’s fecundity and reproductive value, we can predict that men will experience “love at first sight” more often than women. The empirical evidence supports this prediction.” (Buss, 2006: 69)

Australopithecus afarensis (“Lucy”), out with her date around 3.6 mya. This portrayal of an early pairbond is speculative, but it ‘s probably not accurate. Source: AMNH.