"A woman shall not wear anything that pertains to a man, nor shall a man put on a woman’s garment, for all who do so are an abomination to the LORD your God."
Why?
Admittedly, I once owned a pair of distressed, stone washed, paint splattered, boot-cut girl jeans. They looked good and they don't make jeans like that for men. At least not for any less than $200.
When I read this I was not as concerned with how this statement in God's law affects me. Not any more than not wearing any clothing made of different materials or cutting the hair on my temples. (Deut 22:11 and Lev 19:27 respectively.) The death and resurrection of Jesus Christ has taken care of those things. But my concern was with the Israelites who lived with this law.
Was cross dressing a big problem while they traveled through the desert? Was God being proactive against a perversion that was going to happen down the road? And for this act to be an abomination to the Him, that's serious! Or is this statement more about living simply, living true and honestly? In context this verse is surrounded by commands to take care of animals and your neighbors and your neighbor's animals. So it would seem likely that this law, as with most other laws, it is to establish a culture of purity. The law speaks again and again of purging the evil among you. Leaving an injured animal or wearing the wrong shirt is not, itself, evil, though when your eyes are fixed on the things of the Lord kindness prevails and the hottest fashions are not worth worrying about.
Maybe I should be more concerned with how this law does in fact affect me. I no longer own any article of clothing that was intended for a woman, and I don't really intend to purchase such an article again.
May the clothes on your back be a reflection of your love for God. May you never be bogged down by the expected fashions of men, but rather freed by the law and endless love of the Lord.

For 5 seconds my camera allowed me to review this picture before the screen went to black again. But a 5 second review was all I needed to see, and to know, that there was light here. When all I can see is a nearly pitch black room, through the right eyes there is abundant light to be seen.