They are not chosen, they represent an even half, a complete set of chromosomes.
The entirity of a cells genes (found on the chromosomes) is called a genome.
Somatic cells are the cells in our bodies that exclude sperm and egg. Sperm and egg are called germline cells.
The billions of somatic cells in a homo sapien have the same 46 chromosomes. 23 ( half) of them came from dad and 23 from mom. Thus we say somatic cells have two copies of each chromosome and it is abbreviated 2n. The germline cells are 1n or just n.
So your sperm has 23 chromosomes and after sexy time one of them can combine with an egg (which also has 23) to produce a cell(called a zygote) that has an entire complete genome (46). Then that zygote splits, and splits and splits.... And each time before it splits, all 46 chromosomes are copied (the copies are called sisters, or sister chromatids, respective to each other). The cells split into two new cells called daughter cell and each daughter has an entire genome. This form of cell splitting is called mitosis.
Probably the most important event in the cell cycle is the duplication of every DNA stand. This is called a Synthesis (S) phase. This is not a component of mitosis! It's a required event that happens before mitosis. So all 46 chromosomes get copied and then during mitosis each copy (an identical copy) is attached to each other at a region called the kinetachor. A kinetachor attaches sister chromatids (each sister is a copy of each other).
At the beginning of mitosis a web forms in the cell and you can think of the strands that make the web as sliding chains that can pull stuff from the center of the cell to 1 of two perimeter locations (poles) of the cell.
The chain like web attaches to the kinetachor and it rips apart the pair of chromosomes, rips apart the sisters. So that one sister goes to one side of the cell and the other sister chromosome goes to the other side of the cell. So now at opposite sides of the cell you have a complete genome (which will become the new daughter cells).
An identical process occurs in meiosis (specifically meiosis II) which is part of the process that forms the sperm and the egg. During meiosis however there's additional separation (separation of homologs which occurs in meiosis I) that occurs but it's really not pertinent to your question.