"During meiosis I the homologous chromosome pairs separate in a random fashion leading to genetic diversity among the offspring."
It is during meiosis I that segregation of the homologous chromosomes happens. In this phase, all the homologous chromosomes are aligned in the centre of the cell and then pulled apart, each homologous chromosome to an opposite pole of the cell. This allows genetic diversity because is guaranteed that from each of the parents, the offspring only gets one of the homologous pair of chromosomes.