As the property of a neighbour was to be sacred in the estimation of an Israelite, so also the divine distinction of the sexes, which was kept sacred in civil life by the clothing peculiar to each sex, was to be not less but even more sacredly observed. "There shall not be man's things upon a woman, and a man shall not put on a woman's clothes." כּלי does not signify clothing merely, nor arms only, but includes every kind of domestic and other utensils (as in Exodus 22:6; Leviticus 11:32; Leviticus 13:49). The immediate design of this prohibition was not to prevent licentiousness, or to oppose idolatrous practices (the proofs which Spencer has adduced of the existence of such usages among heathen nations are very far-fetched); but to maintain the sanctity of that distinction of the sexes which was established by the creation of man and woman, and in relation to which Israel was not to sin. Every violation or wiping out of this distinction - such even, for example, as the emancipation of a woman - was unnatural, and therefore an abomination in the sight of God.

Deuteronomy 22:11 Parallel Commentaries

Leviticus 19:19 You shall keep my statutes. You shall not let your cattle engender with a diverse kind: you shall not sow your field with mingled seed...