Ooh I actually know this!

When cells split to make new cells, they normally are an exact copy of the old cell. This is mitosis. However, some cells near sex organs undergo meiosis.

The cell has 46 chromosomes. They double, and then some of the DNA gets swapped. The cell then splits into two slightly different cells of 46 chromosomes. This then splits again into two also slightly different cells of 23 chromosomes. Because of the DNA swapping, no two cells have the exact sequence of DNA and are genetically diverse.

When combined with the another sex cell (also genetically diverse from all others in that person’s body) you get a zygote of 46 chromosomes. No two zygote can be the same, even if they are from the same people.

Sometimes a zygote undergoes mitosis and that’s why identical twins are identical because mitosis produces a genetically similar copy. But meiosis doesn’t and that’s why non-identical siblings are genetically diverse.

EDIT: I kept writing gamete instead of zygote. Changed that.