While realizing our own faults, we minimize the extent to which bad characteristics reflected what kind of people we are, predict more improvement than would others with the same faults, claim that others do worse things, and indicate that others are more likely to repeat the same bad behaviors in the future than ourselves

My worst faults and misdeeds: Self-criticism and self-enhancement can co-exist. Gregory S. Preuss & Mark D. Alicke.  Self and Identity, Volume 16, 2017 - Issue 6. http://dx.doi.org/10.1080/15298868.2017.1296019

Abstract: Three studies explored whether self-enhancement is precluded when people recognize or even exaggerate their worst faults and behaviors. Even when acknowledging their faults, participants minimized the extent to which their bad characteristics reflected what kind of people they were, predicted that they would improve more in the future than would others with the same faults, claimed that others have done worse things to them than they have to others, and indicated that others are more likely to repeat the same bad behaviors in the future than themselves. Observers who read actors’ descriptions of their own misdeeds and those of others also saw the things that were done to actors as worse than the things actors had done.

Keywords: Self-enhancement, self-protection, future self, actor–observer, social comparison