Children are born with recessive genes because of meiosis. The human body cells have 46 chromosomes, whereas human sex cells ( egg and sperm) have 26 chromosomes. Each egg and sperm cell have different combinations of genes. When those cells combine to form a zygote, a unique individual is created with a unique combination of DNA. Parents have two genes for each trait and they give on of those genes to their child. If a parent has only dominant genes there is no chance of the child having recessive genes. If a parent has one dominant gene and one recessive gene (heterozygous) there is a 50% chance that the child will receive a recessive gene. If a parent only has recessive genes then there is a 100% chance that the child will have recessive genes. There is the factor of mutations and spontaneous genetic crossover that contribute to the genetic diversity of the individual.
Recessive genes are genes that can only express themselves if their alleles are present in a homozygous condition, i.e. are identical on both the chromosomes. In cases they exist with dominant genes, they will still be there on a genetic level, but have no impact on phenotype.
Transmission of all genes, recessive or dominant, is hereditary. This means that children can be born with recessive genes if one or both of the parents are carriers of recessive genes. The parents might get these recessive genes in turn from their parents.
Sometimes mutations during the birth, during zygote formation, at the embryonic stage or even at later stages in life may be a cause too.