Jamieson, Fausset and Brown on Deuteronomy 22:5

De 22:5-12. The Sex to Be Distinguished by Apparel.

5. The woman shall not wear that which pertaineth unto a man, neither shall a man put on a woman's garment--Though disguises were assumed at certain times in heathen temples, it is probable that a reference was made to unbecoming levities practised in common life. They were properly forbidden; for the adoption of the habiliments of the one sex by the other is an outrage on decency, obliterates the distinctions of nature by fostering softness and effeminacy in the man, impudence and boldness in the woman as well as levity and hypocrisy in both; and, in short, it opens the door to an influx of so many evils that all who wear the dress of another sex are pronounced "an abomination unto the Lord."