there are probably many different takes on this
The movie is based on K.Kesey's famour novel "One flew over the Cuckoo's Nest"
The title is part of a nursery rhyme
which Chief Bromden remembers from his Native American grandmother.
Actually, there is no such thing as a cuckoo's nest. As critics tend to agree, Kesey may have suggested that the lunatic asylum is only a fake because it's supposed to help the people inside, which it does not.
The people that have been committed do not really need medical treatment.They are perfectly normal but the world makes them think they are not, as is the case with Billy.
One also has to keep in mind that since the cuckoo bird borrows other birds' nests, it does not raise any chicks of its own.
The cuckoo's offspring is taken care of by other birds at the expense of the other's birds' offspring, because the cuckoo bird kills them when it hatches.
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hope this helps