The set of lines that shows that Duke Orsino considers men to be more easily swayed by passion than women is this one: "For, boy, however we do praise ourselves, Our fancies are more giddy and unfirm, More longing, wavering, sooner lost and won, Than women's are."
The Duke, who is talking to Viola, is arguing that no matter how much men praise themselves, their "fancies" (their whims, their desires) are more "giddy" (more frivolous, more euphoric) and "unfirm" (more unsteady, since they are not firmly set), more "longing" (more craving), "wavering" (more quivering, more fluctuating), sooner lost and won (that is to say, temporal, brief, fleeting) that women's fancies. Because of this, they are more easily persuaded by passion, due to the intense, strong, enthusiastic, and uncontrollable nature of this feeling.
