The woman shall not wear that which pertaineth unto a man, neither shall a man put on a woman's garment: for all that do so are abomination unto the LORD thy God.
Even if someone were to rely on modern translations (which are made from the same Hebrew text in this instance), he would come to the same conclusion about what it says:
NASV A woman shall not wear man's clothing, nor shall a man put on a woman's clothing; for whoever does these things is an abomination to the LORD your God.
NIV A woman must not wear men's clothing, nor a man wear women's clothing, for the LORD your God detests anyone who does this.
We see nothing in the verse about Canaanite worship or women in the military or transvestism. It is about as straightforward as it can get.
Even further, and this is important, the verse doesn't say, "women, don't look like men," "men, don't look like women," or "you've got to be able to tell the difference between men and women." Those are only means by which someone can ignore the verse. It also doesn't say, "This issue is a joke!" Which is the most common argument that I hear. Or another version of the same argument, "This is so stupid!" Given by outstanding Bible scholars.
In almost every case, I've found in a debate or discussion over Deuteronomy 22:5 that those who do not want to obey it will start with arguing about what it means. Once they find out that they can't get any traction there, then they argue about the application. When someone has been unbiased and without predisposition in studying a passage, he won't discuss or debate this way. He starts from scratch with the desire to understand the meaning and the application, not explain it away.
I've dealt with the interpretation of Deuteronomy 22:5. Now I will show you that women in dresses and skirts and men in pants is how that it has been practiced. I'm just the messenger. I think men and women are equal. They have differing roles. The differing roles are seen in their distinct design. Men and women are different. God wants those differences reflected in designed distinctions in their clothing. Western civilization and particularly the United States practiced these designed distinctions. They still have never been replaced with other designed distinctions. This is reflected in the comment of experts in the history of fashion.
Kidwell, Claudia Bush Kidwell and Valerie Steele write in Men and Women: Dressing the Part (pp. 2-14):
In analyzing gender identities, we use the term gender conventions to refer to the social and cultural expectations of behavior, clothing, and images that have divided men and women into separate spheres. . . . [T]he existence of these behavioral standards has always been an integral part of our social structure. . . . When we examine how clothes define an individual, we must also set the man or woman within the context of their (sic) place and time. . . . The full impact of these gender conventions on fashion is only revealed when the two sexes in fashion history are examined side by side. It then becomes obvious that historically clothing has served to separate men and women. . . . Consider the image of a woman dressed in pants. It is a clothing symbol laden with gender meaning. . . . The most obvious division in clothing today is between trousers and skirts. . . . In Europe, over the centuries, flowing robes became associated with femininity and tailored trousers with masculinity. . . . Women in Europe did not wear trousers because the garment had acquired such strong masculine connotations.
Allison Lurie in The Language of Clothes (p. 224) writes:
Real trousers took much longer to become standard female wear. It was not until the 1920s that women and girls began to wear slacks and even shorts for sports and lounging. The new style was greeted with disapproval and ridicule. Women were told that they looked very ugly in trousers, and that wanting to wear The Pants in our culture, for centuries, the symbolic badge of male authority, was unnatural and sexually unattractive. . . . This freedom, however was limited to the private and informal side of life. Wearing slacks to the office or to the party was out of the question, and any female who appeared on a formal occasion in a trouser suit was assumed to be a bohemian eccentric and probably a lesbian. . . . At Frick Collection library in New York (in the 1960s) women [were] not admitted unless they [were] wearing skirts; a particularly ancient and unattractive skirt [was] kept at the desk for the use of readers ignorant of this rule.
Ann Hollander in Sex and Suits: The Evolution of Modern Dress (p. 53) writes:
Trousers for respectable women were publicly unacceptable except for fancy dress and on the stage, and they were not generally worn even invisibly as underwear until well on in the nineteenth century. At that period the common adoption of underpants by women seems to represent the first expression of the collective secret desire to wear pants, only acceptably brought out on the surface with the bicycling costumes of the 1890's, and only finally confirmed in the twentieth century with the gradual adoption of pants as normal public garments for women. . . . Pants were still a forbidden borrowing from the male, so unseemly that they could only be generally hidden until their time finally came.
The movement away from gender distinct dress has been termed the "unisex movement." This movement was a purposeful erasing or blending of the delineating lines between male and female appearance. An article in the 1970 Compton Encyclopedia Yearbook states, "Paris couturer Jacques Esterel states that identification of the sexes in terms of clothes will become a thing of the past. He designed an identical tunic and pants outfit for father, mother, and child . . . unisex clothes." In Life magazine, January 9, 1970, Rudi Gernreich writes, "When proposing his vision of the future of fashion in 1970, he predicted that the traditional apparel symbols of masculinity and femininity would become obsolete, . . . women will wear pants and men will wear skirts interchangeably. The pant-skirt controversy is a male-female role controversy." Kidwell and Steele write (p. 144):
Controversial fashion changes such as women adopting trousers can only take place after women's roles in society have altered. The mass acceptance of a style may accompany a change in public opinion, but does not precede it. Dress reformers were correct in seeing the connection between women's roles and their clothing, but erred in believing that by changing the costume, changes in gender conventions would automatically follow.
Our country practiced the pants as male dress and the dress or skirt as the female dress. Those were the designed distinctions. None other served as the distinction between the genders. They were erased by the culture because the culture didn't care to keep those distinctions any longer, despite what God had said. They were replaced by nothing.
For more information on this topic, read the study here.