Because at the moment of conception, that sex cell (one sperm or one egg) will merge with the other person's sex cell (one egg or one sperm) to form a complete set of genes, and voila, there is a fertilized egg leading to a new and unique person.
Before you are born, when your sex has been established, you have sex cells that only contain 23 chromosomes. All your other cells have 46 chromosomes, but the special sex cells undergo meiosis, and get further halved to 23.
Then you grow up and get married, and during conception, your sex cell merges with your partner's sex cell and now the new cell has 46 chromosomes, but half are your chromosomes and the other 23 come from your sex partner. This newly fertilized egg has 46 chromosomes and develops into a new person.