The woman shall not wear that which pertaineth unto a man, neither shall a man put on a woman's garment: for all who do so are abomination unto the LORD thy God.
My first reaction was: yikes, "abomination" is a pretty strong word! But many other things are described as "abominations", including, for instance, many things I eat ( Deut 14:3, all of Lev 11). This chapter itself also includes many restrictions that seem simply bizzare ( Deut 22 :9-12). Read through Leviticus, Deuteronomy, and so forth, and you find yourself overwhelmed by commands to make sacrifices, to observe countless rituals, to abstain from things with no imaginable moral purpose - countless things that are completely foreign to a Christian. It sure puzzled me when I was a new Christian. So, what on earth is going on here?
The short answer is: This is the Jewish Law, the Law of Moses. We, as Gentile Christians, are not called to follow this law. Christ did not call us to become Jews; He called us to salvation through Himself. This is not a liberal doctrine, a conservative doctrine, a Protestant doctrine, or a Catholic doctrine; it is a Biblical doctrine, and one of the main themes of the New Testament. See, for example, Acts 15, Colossians 2,, and Galatians 2-6. It is not even the case that God would prefer that we follow this law, but has "let us off the hook"; in fact, Paul strongly warns the Galatians against returning to the law of circumcision, the law of the flesh. That is why pig meat, an "abomination" for those under the law, is no sin for us; likewise, I am convinced, for crossdressing.
So am I saying that Deuteronomy, Leviticus, etc. are wasted ink? No, not at all. They tell us how God prepared the world for Christ's coming, by teaching men to worship Him with a fleshy, ritual law. They also provide wonderful illustrations of how to "love our neighbor as ourself": see, for instance, Deut. 24:10-23. There is plenty of wonderful stuff in these books; we just have to remember that the ritual law is not our law. I will stop here, but I could go on; if you want to talk more about the role of the law, I will, or you could ask your pastor. If you're shy, you could ask why (for instance) we are not under the dietary restrictions, or why we don't wear blue tassels on our clothing ( Numbers 15:38-9 and Deut 22:11).
Finally, if you're interested in some Biblical commentary on this verse, you can check out Myschel's commentary research. I find it unnecessary - when God releases us from the Law of Moses, that's that, regardless of what the commentators say - but I know some of you want something more. My friend Myschel slaved over dusty tomes to oblige you, so dig in and see what the Biblical scholars have to say about Deut. 22-5.