Drawing parallels between human cognition and artificial intelligence, we explored how large language models (LLMs) internalize identities imposed by targeted prompts. Informed by Social Identity Theory, these identity assignments lead LLMs to distinguish between "we" (the ingroup) and "they" (the outgroup). This self-categorization generates both ingroup favoritism and outgroup bias. Nonetheless, existing literature has predominantly focused on ingroup favoritism, often overlooking outgroup bias, which is a fundamental source of intergroup prejudice and discrimination. Our experiment addresses this gap by demonstrating that outgroup bias manifests as strongly as ingroup favoritism. Furthermore, we successfully mitigated the inherent pro-liberal, anti-conservative bias in LLMs by guiding them to adopt the perspectives of the initially disfavored group. These results were replicated in the context of gender bias. Our findings highlight the potential to develop more equitable and balanced language models.