(ה) לֹא־יִהְיֶ֤ה כְלִי־גֶ֙בֶר֙ עַל־אִשָּׁ֔ה וְלֹא־יִלְבַּ֥שׁ גֶּ֖בֶר שִׂמְלַ֣ת אִשָּׁ֑ה כִּ֧י תוֹעֲבַ֛ת יְהוָ֥ה אֱלֹהֶ֖יךָ כָּל־עֹ֥שֵׂה אֵֽלֶּה׃ (פ)
(5) A woman must not put on man’s apparel, nor shall a man wear woman’s clothing; for whoever does these things is abhorrent to the LORD your God.
What you can and can't wear
(א) שלא ילבש איש מלבושי אשה - שלא ילבשו האנשים מלבושי הנשים, ועל זה נאמר (דברים כב ה) ולא ילבש גבר שמלת אשה.
(1) That a man should not wear the clothes of a woman: That men should not wear the clothes of women, and about this it states (Deuteronomy 22:5), "and a man should not wear the garment of a woman."
(א) שלא תלבש אשה עדי איש - שלא ילבשו הנשים מלבושי האנשים ולא יזדינו בזינם, ועל זה נאמר (דברים כב ה) לא יהיה כלי גבר על אשה. ותרגם אונקלוס לא יהא תקון זין דגבר על אתתא (עי' נזיר נט א). ומן הדומה כי מפני כן פירש הכתוב בכלי זין, לפי שהם הכלים המיחדים לגמרי לאנשים, שאין דרך אשה בעולם לצאת בכלי זין, אבל הוא הדין שאסור להם מדאוריתא לצאת במלבושים שדרך האנשים באותו המקום להשתמש בהם, כגון שתשים בראשה מצנפת או שאר כלים המיחדים לאיש (עי''ש בתרגום יונתן בן עוזיאל).
(1) That a woman should not wear the adornments of a man: That women should not wear the clothing of men and not arm themselves with their weapons. And about this it states (Deuteronomy 22:5), "There shall not be the vessel of a man upon a woman." And Onkelos translated [it], "There shall not be a weapon of a man upon a woman" (see Nazir 59a). And that which is similar [is also prohibited]; since this is the reason that [Onkelos] explained Scripture as regarding weapons - because they are vessels that are completely unique to men, as it is not the way of a woman in the world to go out with weapons. But the same is true, that it is forbidden from the Torah, for them to go out with clothes that it is the custom of the men of that place to use - for example, that she should place a turban on her head or other vessels that are unique to a man (see Targum Jonathan on Deuteronomy 22:5).
10 commandments
Lo Tachmod which is don't covet connects to my theme of cross dressing because covet means to posses something like you want it so this connects because you're doing something Hashem doesn't approve but you want to cross dress because that is the way you like to dress
(א) לא יהיה כלי גבר על אשה. (נזיר כט) וכי מה בא הכתוב ללמדנו? [אם] שלא תלבש אשה כלים לבנים, ואיש לא יתכסה בגדי צבעונים, (ת"ל) [הרי כבר נאמר] "תועבה", דבר הבא לידי תועבה! [אלא] זה כללו של דבר - שלא תלבש אשה מה שהאיש לובש, ותלך לבין האנשים; והאיש לא יתקשט בתכשיטי נשים, וילך לבין הנשים.
(1) (Devarim 22:5) "A man's vestment shall not be upon a woman": What does Scripture come to teach us? If that she should not wear colored clothing, is it not written (Ibid.) "for the abomination, etc."? And this is not an abomination. It means, rather, that a woman should not wear what a man wears and go among the men (for licentious purposes), and a man should not wear colored clothing and go among the women.
Dvar Torah
A man can't wear women's clothing because cross dressing leads to inappropriately actions and also vise versa with women. In addition for a man even putting on a women's clothes will lead him to having sinful thoughts. This is why we must distance ourselves from cross dressing Rabbi Menachem Mendel has an opinion that a man has a beard he can not shave it because its like a women shaving. A mans arm is different to a women's arm. This is why we should stay away from cross dressing.
http://www.chabad.org/library/article_cdo/aid/970805/jewish/Cross-Dressing.htm
