Complex sentence: An alternative version of the theory of the self-serving bias states that the bias does not arise because people wish to protect their private self-esteem, but to protect their self-image (a self-presentational bias).
Split into simpler sentences: An alternative version of the self-serving bias states that the bias does not arise due to the fact that people wish to protect their self-esteem. Instead, people wish to protect their self-image (a self-presentational bias).