I don't know if this totally answers your question but sex is actually determined by the male haploid cells (sperm). Females have XX chromosomes and thus can only produce daughter haploid cells with X chromosomes. Males have XY chromosomes and produce daughter haploids cells with either X or Y chromosomes. The sex of the fertilized zygote is determined by whether an X or a Y chromosome containing sperm reaches the egg.

Besides what other response have said, the X chromosome passed from a mother to an offspring is not typically identical to either of the X chromosomes in her own body. Rather, the X chromosome passed on through her eggs is a blend of her two X chromosomes. This process is called genetic recombination and is basically what allows sexual reproduction to roll new genes.

Since men (typically) only have one X chromosome to start, the X passed in their sperm is identical to that of their somatic cells. So two sisters with the same parents will share one identical X from their father, but the second X from their mother will be different combinations of her two X's.

Edit to add: if genetic recombination didn't happen, then lots of siblings would end up as genetic twins. (50% chance within the same gender). And that would also be identical to the offspring from one crossing one grandparent on each side... Fortunately this doesn't happen!

Women require a man to contribute before they can give birth

I was thinking the same sort of things but my understanding was the sperm that carries the determination of sex not the egg.