why does "crossing over" involve non sister chromatids(homologues) instead of sister chromatids?

One homologous chromosome is inherited from the organism's mother; the other from the organism's father.

A sister chromatid is a duplicate of itself and it occurs in mitosis. Homologous chromatids are one from each parent and this happens in meiosis.You can't cross over with yourself, crossing over aids in random assortment of the daughter cells or offspring.

It does not involve incest.

The phenomenon of "crossing over" involves non-sister chromatids, specifically homologous chromosomes, instead of sister chromatids. This is because crossing over is a process of genetic recombination that occurs during meiosis, the specialized cell division that produces gametes (sperm and eggs) in sexually reproducing organisms.

During meiosis, homologous chromosomes pair up, aligning with each other, and exchange segments of genetic material. This exchange occurs at specific points called chiasmata, where non-sister chromatids of homologous chromosomes overlap and break and then reconnect with each other.

The reason why crossing over occurs between homologous chromosomes and not between sister chromatids is due to their structural and genetic differences. Homologous chromosomes are pairs of chromosomes, one from each parent, that have similar but not identical DNA sequences. They contain the same genes, but each gene may have different versions, called alleles, due to genetic variations.

On the other hand, sister chromatids are two identical DNA molecules produced during DNA replication that are bound together at the centromere. They are formed prior to the start of meiosis when DNA is replicated in the S phase of the cell cycle. Sister chromatids have the exact same genetic information because they are replicated copies of the same chromosome.

Crossing over between non-sister chromatids of homologous chromosomes is crucial for genetic diversity because it generates new combinations of alleles. This process results in the shuffling and mixing of genetic material between homologous chromosomes, leading to the creation of unique combinations of genes that are different from those of the parent chromosomes.