What is the origin of the term pigeon pair? What context can I use it in?

Answer 1

A boy and girl, twins. It was once supposed that pigeons always sit on two eggs which produce a male and a female, and these twin birds live together in love the rest of their lives

Context:
For the coveted mother of a pigeon pair, the sweetness is doubled.

Answer 2

if someone has two children, whether they are twins or not, and ideally if the boy is the elder it is said to be the perfect pigeon pair.

So if you or someone you know has two children and they are a boy and a girl you could say they are a pigeon pair.