Why is cross-dressing forbidden?
Maimonides, in his law code Mishneh Torah, lists the cross-dressing prohibition of Deut. 22:5 (which forbids women wearing clothes that are ordinarily worn only by men and vice versa) under the category of laws relating to idolatry and the customs of the nations. This suggests that cross-dressing may have been associated with some type of idol worship, or may have been practiced by some group of idolators, and was forbidden by the Torah as a guard against these practices. Note that what is forbidden by this law is only the wearing of garments that are ordinarily worn ONLY by members of the opposite sex. Thus the prohibition depends on how people dress in a given country at a given time. If the wearing of skirts by men became widespread (like the wearing of kilts by Scotsmen), it might no longer be forbidden.