How come you can never have identical twins who are the opposite sex?

I suppose because if you could they would not be identical would they? That's a layman's answer.

The correct name for identical twins is monozygotic twins. The first part mono- means one and the second, -zygotic, refers to the zygote: the single cell formed when the sperm fuses with the ovum. So indentical twins come from the same zygote. At some point when it was dividing it divided into two and both went on to become humans. If the division is not complete you get conjoined twins.

Because they come from the same zygote they have exactly the same genotype and thus the same sex chromosomes. They, therefore, must both be male or female.

Dizygotic, non identical twins also called fraternal twins, come from two zygotes: two ova each seaparately fertilsied by a sperm. They come from the same pregnancy but are as different as they would have been from separate pregnancies.

Simple,

Identical twin will have exactly the same genetic material. If they were to be of opposite sex, one would have had to inherit a "Y" chromosome from the father making him a male and the other would have had to inherited an "X" chromosome from the father. They would no longer be "identical" twin. Also males and female are morphologically different, so even from that view point they are not identical. 

It's because since they come from a single fertilized egg which splits in two, they share the same genetic material, or in scientific terminology, identical DNA (deoxyribonucleic acid). Includes the same gender genes, either female (XX) or male (XY). 

Because they're identical.

A male and a female can never be identical - are anatomically and morphologically different.

Because identical twins are the result of a single fertilized egg splitting into two during development, resulting in 2 embryos with identical genomes. That means both embryos have the same chromosomes. Since gender is determined by whether an embryo has 2x or 1x and 1y chromosomes, both of the twins must be the same gender. 

I think there a difference between boys and girls, biologically.

Well . . . duh!

duh... if they are different sexes, they are not identical, are they?