Olivia's analysis that the narrator is insecure seems to be better supported by the details provided, such as the defensive stance and preoccupation with others' perception indicated in the text excerpts.
The question seems to be asking for an analysis of a narrator's personality based on their internal monologue and other provided text excerpts. From the information given, it appears that Olivia, who argues the narrator may actually be “insecure,” has provided the best details to justify her views. For instance, the narrator's constant defensive stance and rehearsed mental retaliations as described in one excerpt suggest a preoccupation with how others perceive them and a readiness to defend against perceived attacks, which may indicate insecurity. Additionally, the reference to self-serving bias in the context of actor-observer bias suggests that the narrator may be trying to protect their own ego, which is another sign of insecurity. In contrast, Katie's view that the narrator is “impressed with himself” could be seen as less grounded in the text, unless further details that support self-admiration are provided.