Why is an illegitimate child called a love child?

Answer 1

One answer:

It is what we call a "euphemism," which is a polite way of saying something society regards as unpleasant. For example, instead of saying someone is dead, we say they "passed away." Back in the old days, all public discussions of sex were considered rude or inappropriate; even newspapers and magazines were not supposed to mention it, except indirectly, by using euphemisms. So, an illegitimate child came to be known as a "love child" because it sounded more polite and less controversial. The expression was especially promoted by tabloid and scandal magazines in the 1950s and beyond, because it allowed them to mention that a celebrity had given birth to a child out of wedlock, which in those days was considered outrageous. It thus associated sex and pregnancy with love, rather than with illegitimacy.

Another answer:

Because it has a kicky, positive sound. Love, Child! one can visualize stylized flowers in the flower-girl tradition. Certainly it sounds much better than a curse word that means illegitimate child, you know, the B word. Love Child might derive from French, Enfant D"Amour- Child of Love.