Freud's psychosexual theory of development has several stages and lots of elements within those stages. The term anal-expulsive refers to a time during the anal stage of development (which lasts from about 18 months to three or four years old) in which the focus of pleasure is the anus and children find sensual pleasure in having bowel movements (expelling feces). This is the opposite of anal-retentive in which children retain feces (they resist having bowel movements).
Freud believed that a child who does not successfully take control over their sphincter at the anal stage will become fixated and may end up with a anal-expulsive personality - which includes being disorganized, messy, careless, rebellious, and sometimes cruel.
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