Men tend to want the woman they see in front of them, while women want the man other women see:

Are women more interested in men who are already in a relationship? Female and male participants who were single or in a relationship viewed information about an opposite-sex other and indicated their interest in pursuing this target. Half of the participants were told that the target was single and half read that the target was currently in a relationship. The results showed that only single women were more interested in pursuing an attached target rather than a single target. …

According to a recent poll, most women who engage in mate poaching do not think the attached status of the target played a role in their poaching decision, but our study shows this belief to be false. …

Across ten world regions, 57% of men and 35% of women indicated they had engaged in an attempt at mate poaching, … people who mate poach are more likely to be low in agreeableness and conscientiousness than those who do not. …. Research on animal mating (e.g., fish, birds) has shown that female animals are more likely to choose a male that has already been chosen by other females … Research on human preferences does show that women rate men as more desirable when they are surrounded by other women, compared to being alone or surrounded by other men. Conversely, men rate women as less desirable when they are surrounded by other men, compared to being alone or surrounded by other women.

Yet another way in which we don’t know why we do what we do.