The textbooks say that children display "egocentrism" - as if this were different from the plain old egotism of adults! The fact is, we cowards refrain from saying children are egotistical because it doesn't seem right to condemn normal behaviour.
"Egocentrism" says that it is acceptable to be egotistical about helping others, as opposed to serving only oneself. It is designed to do away with the more nasty and inconsiderate word "egotistic".