The question effectively asks why cats are white all over. It is because they have a dominant gene symbolised by the letter W which removes pigment from the hair strands. It does this by removing the pigment creating cells in the skin. These are called melanocytes. Genes are on chromosomes and chromosomes are in the DNA of cats. The DNA is in the nucleus of the cells of the cat.
Genes instruct how cells are created during the embryonic stage of development of all animals. They determine all aspects of an animal’s characteristics including hair colour. So, for example, a human has blond hair because of the hair colour gene, known as MCIR.
The gene masks all other colours (epistatic – the suppression of the effect of one such gene by another). The dominant white gene as it is called is present at a separate locus to the piebald gene (white spotting gene) and therefore not dependent on the piebald gene (i.e it is not an allele of the piebald gene).
The dominant white gene can also make cats deaf and the eyes are often blue (without iris pigment) or odd-eye colour (different coloured eyes, one blue and one yellow).
A survey of 185 white cats found that 25% had yellow eyes and normal hearing, 31% had blue eyes and normal hearing, 7% yellow eyes and were deaf and 37% had blue eyes and were deaf. The deafness is “associated with degenerative changes in the succule and cochlea” (Robinson’s Genetics).
Partly white cats
If the question was asking why cats have some white in their coats, it is because they have the piebald or white spotting gene. The classic cats which have the piebald gene are bicolour cats – white and another colour. However, there are millions of variations and other coats where areas of white fur are seen caused by the presence of this gene in the cat’s DNA (i.e. “lockets” on the chest and “gloving” on the lower leg). Breeders or geneticists grade the variations of expression of the gene from 1 to 10 where 2 is a near black cat with small spots of white and 9 is a near white cat with small spots of black.
In short the answer to the question in the title is “because of genes”.
P.S. Dalmatian dogs are bicolored. They too can be deaf. There are multiple causes the Kennel Club says. I’ll add my thoughts: the piebald gene is the cause or a contributing factor.