Women and men cross-dress for very different reasons, to the point that in many cases what a particular society considers transvestitism will be different for each gender. This explains the variation of both the nouns and the verbs in sections 1a and 1b of Deut 22:5. The verse is much more than a simple prohibition of particular wardrobes, and indeed in no way addresses the issue of women wearing masculine garments, since in the culture of ancient Israel the clothing of men was less associated with gender than was the clothing of women. Rather, the verse reflects the most basic ideology of gender in Israelite society, and to this end it distinguishes not simply between male and female but also between different qualities of men. The ideals of manhood and masculinity were not considered either simple or innate; one had to achieve them through action, behavior, and a good relationship with Yahweh.
Harold Torger Vedeler, “Reconstructing Meaning in Deuteronomy 22:5: Gender, Society, and Transvestitism in Israel and the Ancient Near East,” Journal of Biblical Literature 127, No. 3 (Fall 2008), 473.