Why sister chromatids and daughter cells but not brother chromatids and son cells?
During the days when philosophers used to debate, they tended to regard  reproduction as a feminine trait. So naturally organisms/cells capable of producing offspring are also given a feminine trait. The parent cell is often called the mother cell, and the daughter cells are so named because they eventually become mother cell themselves. 

I presume there exists a similar argument for sister chromatids, in that they are identical. When they separate, they are usually termed as undivided chromosomes.