"Birds of a feather" is from the proverb "Birds of a feather flock together," meaning that similar people congregate. In old poetic English, "birds of a feather" means birds which have the same kind of feathers, so the proverb refers to the fact that birds congregate with birds of their own species. This proverb has been in use since the 16th century.

Birds of a feather: people of the same sort (they are similar in a particular way) Birds of a feather flock together: people of the same sort are found together

matching pair: twins, close friends, com-padres, comrades, couple, friends, matching set, pair, peas in a pod, two minds thinking as one, two of a kind

Birds of a feather flock together. ..of a feather = of the SAME feather. Flocks of birds are the same species. That is, they carry the same feathers. The expression is used for people who share a common mentality, usually idiots actually. Have you noticed how the idiots seem to gather together? Other examples: ESL teachers in China; ESL teachers in Japan.

Two people who share many commonalities.