A common wisdom is that women are more dovish and less militaristic than men, so that they are more inclined to disapprove the use of military force on one hand, and to support peaceful resolutions on the other hand. In this paper I present findings from Israel that challenge this theory, revealing that women are less inclined to support the use of military force, but at the same time they are also more hawkish regarding territorial compromises. As an explanation I focus on the role played by the psychological mechanism of risk aversion in shaping individual's attitudes toward war and peace under intractable conflicts, and in particular on the varying levels of risk aversion that lead to gender gap(s) in security preferences. The assumption that women choose to avoid the necessary costs of war and tend to prefer the less "costly" peaceful solution, ignores the not-so-small potential risks deriving from any peace plan. The consequences of failed peace negotiations can be a deterioration of the situation into a violent episode that would not have occurred had the status-quo remained. Since women are known to be more risk averse than men, they tend avoid the risk of peace resolution just as they avoid the risk of war. Using survey from the years 2001-2019, I examine this hypothesis within the context of the Israeli-Palestinian conflict, in which attitudes toward military actions, the usage of violence and peace plans constitute a major part of public opinion and everyday life.