Final answer:
Genetic variability can still occur without crossing over, as the process is one of several mechanisms that contribute to genetic diversity in offspring. Crossing over during prophase I of meiosis increases genetic variation but is not the only source of such variation.
Step-by-step explanation:
The statement 'Genetic variability will not occur among offspring if crossing over does not occur during prophase I of meiosis' is false. Crossing over is a process that occurs during prophase I of meiosis, where there is an exchange of genetic material between non-sister chromatids of homologous chromosomes. This leads to a recombination of genetic material, increasing the genetic variation in the resulting gametes. However, while crossing over significantly contributes to genetic diversity, it is not the sole mechanism for creating variability. Independent assortment during metaphase I of meiosis also contributes to genetic variation by producing different combinations of maternal and paternal chromosomes.