Cocky is a slang term used in the USA and UK to mean 'acting above one's station', 'arrogant', 'bold', or 'impudent'. It is not necessarily an insult, but does suggest that one's opinion of oneself does not match the reality.
While this is indeed derived from the attitude and bearing of a male chicken, the double entendre tying it to the male genitalia is apparent. This may explain why it is used most often to refer to males.