Based on my general interpretation of Jane Eyre, Mr. Brocklehurst thinks that it is morally just to treat Jane badly because of what her aunt had falsely claimed about her (that she is a delinquent). Unlike Helen, a character portrayed in the novel as a kindhearted & forgiving Christian, Brocklehurst is a strict Christian who believes that the students who behave deserve to be treated well, whereas the troublemakers deserve bad treatment.
The fault that Brocklehurst possesses is the inability to sense the extent to which a faulty person can be punished. His (wrong) religious views cause him to be overly hypocritical of others' mistakes and, because of that, he is easily tempted to humiliate them for their mistakes. In other words, even though he attempts to spread morality around the school, he is actually doing the opposite.
Hope this helps! :)
