be someone's pigeon be someone's concern or affair.
☞ In this phrase, the word pigeon derives from pidgin, as in pidgin English, the term for a grammatically simplified form of a language used for communication between people not sharing a common language. Pidgin itself represents a Chinese alteration of the English word 'business': it entered the English language with the meaning 'occupation' or 'affair(s)' in the early 19th century, emerging from the hybrid of English and other languages used at that time between Europeans and the Chinese for trading purposes.