Why we call the cell produced as the result of fission as 'daughter' cells and the homologous chromatids as 'sister' chromatids rather than the word 'son' or 'brother'?
Since time immemorial reproduction has been regarded by philosphers as a feminine trait as giving birth has been the prerogative of a female. Hence organisms and cells capable of producing offsprings are termed as a feminine trait.
Based on this, the parent cell is called the mother cell, and new cells so made are called daughter cells as they further carry on the process of division further to become mother themselves, and the cycle goes on.
The duplication of the chromatids is based on a similar argument. As identical chromatids are produced they are termed sister chromatids and not brother chromatids as reproduction is considered as a female trait.