Final answer:
Cells are arrested in mitosis during metaphase for karyotype analysis because that is when chromosomes are condensed and visible, allowing for clear identification and arrangement into a karyotype.
Step-by-step explanation:
The cells must arrest in mitosis for karyotype analysis because it is only during mitosis, specifically in metaphase, that the chromosomes are highly condensed and visible with a light microscope. At this stage, the chromosomes are easiest to distinguish from each other because they are at their most compact form. This visibility allows geneticists to use staining techniques like fluorescent dyes and chromosome painting to create a karyotype, which is an organized profile of an individual's chromosomes.