Perhaps, we can turn the question around, as Menninger did in a number vignettes in Chapter 7: Why would individuals resist wrongs (committed as part of a group)?
Menninger recounted the story of a Dominican friar, Antonio de Montesinos, who, in 1511, preached against putting the Indians of Hispaniola into slavery. He and his monastery stood firm until word was sent to the King of Spain. The learned men of the Spanish Church (of great influence at the time) rebuked Montesinos for his error.
The monastery had a conscience. The King of Spain and his courtier scholars did not. Shame on them.
This example shows why it is so easy to criticize Christianity. Some Christians are always seeking accommodation with “the Powers that Be”. “The Powers that Be” act without conscience. Christians (as a group) get the blame.
This points out the obvious advantage to group-think: Group-think allows you to act without conscience. Even better, to the extent that you buy into the system, group-think will exchange your old traditional super-ego (a system of tautologies that mark what is good and evil, formed from family, faith, community and guild) with its own (system of tautologies).
This offers an answer to the question: Why would individuals want to commit wrongs (as part of a group) that they never would have committed as individuals?
Answer: These individuals would have committed the wrongs on their own, if they lacked (what a Christian would call) “conscience”.