For follow-up discussion and general commentary on the topic. Comments are sorted chronologically.
Believe it or not, this was almost an article of faith where I went to Bible College, in the '70s.
Col 2:17 tells us that these laws are all shadows of some greater spiritual reality. We err when we claim that our 3-D world is reality. Paul speaks of spiritual things having 4 dimensions (Eph 3:18), modern physics believes there are 11. Both teach that our 3D world is only a shadow or projection of some greater reality. It takes some digging to find the meaning of some of these shadows because for many an explicit statement of their meaning does not exist in scripture.
Contrary to the most common belief among Christians, the soul and spirit are not the same thing. Both the Old and New Testaments are explicitly clear about this, but most Christian denominations prefer the Greek teaching that these things are synonymous. In scripture spiritual things are represented by males, by birds, by barley, by linen and other symbols. Each of these symbols is paired with another symbol. In the case of birds, with another bird representing good and evil spirits. With the other symbols the converse is either the flesh, or the soul. These two are also not the same but are generally closely linked because the soul (not life as normally translated) is in the blood of the flesh (Gen 9:4, Lev 17:11, 14, Deut 12:23).
Soulish things are not to be mixed with spiritual things. We are given these types because we do not have the senses necessary to directly observe the spiritual realities, but as we become more spiritual through the sanctification process we can begin to indirectly perceive the spiritual. At such time we are to give up the "childish things" (1 Cor 13:11). At no time is it proper to mix the two, yet many Christians try to mix them all the time, or worse, claim to be spiritual but never move beyond the "women's clothing" they have been wearing from the beginning of their spiritual journey.
Revelation 19:8 tells us that the fine linen of the garments worn by the resurrected saints is their righteous acts. Ezekiel 44 speaks of this in a little more detail in that picture of the New Covenant temple in heaven. The corrupt Levitical priests are limited to the outer court (physical world) and wear woolen garments. Their garments are not righteous acts; they are fitting for the lesser understanding and ability in spiritual matters of the newly born again sinner. They bear a close resemblance to the garments God made for Adam from ram's skins. These garments are never to be worn inside the temple in the direct presence of God.
The Zadok (Melchizedek) priests have two sets of garments. When they enter the temple and minister directly to God they must wear the linen garments, but when they leave the temple and go to minister to the people in the outer court they must remove their linen garments and put on woolen garments. 2 Cor 5 gives further insight into this in the discussion of the fulfillment of the Feast of Tabernacles and our receiving the glorified (resurrection) body. When Jesus received this spiritual body he appear from nowhere in the upper room when he put on the woolens and disappeared from sight when he replaced them with linens.
Beyond these examples we have no idea how this works, but this is what it means when God tells men not to wear that which pertains to women and vice versa.
"Modest apparel" (KJV) and "proper clothing" come from the Greek words, "kosmios katastole". "Kosmios" means orderly, well arranged, decent, modest. "Katastole" refers to a garment, the word being derived from the verb meaning ‘to send or let down, to lower’ (kata, "down," stello, "to send"). By its meaning, it is believed to refer to a long, flowing garment.
Wearing only dresses maintains the clear distinction in dress taught in Deuteronomy 22:5. When women always wore dresses and men wore pants, there was a clearer distinction between the sexes. The significant difference in external clothing affirmed the significant differences in God given roles.
The adoption of pants by women was brought about by the early women’s rights advocates, women wanting to eliminate or obscure all God ordained differences between the sexes. It was these same women who advocated sexual freedom for women (aided by both birth control and abortion), and tried to encourage women to forsake their traditional roles of wives and mothers.
Though women today wear pants almost as much as men, still our culture views pants as men’s clothing. Look at the restroom signs. Consider expressions we still use, like, "Who wears the pants in the family?" By this we mean who is the true leader of the family (the role God ordained for the husband, but often usurped by the wife)."
The issue of woman wearing is not always an issue of erasing gender distinctions. Sometimes slacks are more modest. Some situations arise in which dresses or skirts expose more of women's immodest parts to the public.
1) Woman's slacks actually cover more.
2) Women's slacks do not look like men's.
3) Customary clothing DOES change. Should men return to wearing robes as in biblical times? Men's and women's robes were once closer to one another than we might imagine.
Very good point Larry. Men did not wear slacks in Israel or Egypt at the time this law was given on Sinai. That cannot be what this law is about. The men of Israel and most, if not all the surrounding nations wore robes or shorter skirts at this time. Slacks were not worn until much later and were developed farther east in Mesopotamia or Persia (I don't remember which) and their use spread from there.
When men needed to do heavy work they would either strip down to their skivvies or "gird up their loins", raising their skirts to their waist and tying them up to keep them out of the way.
To the eye of the 21st Century westerner the difference between male and female dress of that age is not distinguishable because we generally do not know the subtle differences in style and stitching that made the difference between a man's clothing and a woman's clothing. Since clothing does not survive well even in that dry desert environment I am not even sure that archaeologists really have much understanding of these differences.