Final answer:
The independent assortment of allele pairs occurs due to the separation of homologous chromosomes during anaphase I of meiosis, which is essential for genetic diversity. Hence, the correct option among the given ones is Option E.
Step-by-step explanation:
The independent assortment of allele pairs is due to E which states the independent segregation of homologous chromosome pairs during anaphase I. During meiosis, specifically in anaphase I, homologous chromosomes separate and are randomly distributed to the daughter cells. This process contributes to genetic diversity by ensuring that each gamete, or sex cell, contains a unique set of genetic information. The chromosomes align randomly during metaphase I, and their separation during anaphase I contributes to the independent assortment of genes.