The emergence of Large Language Models (LLMs), has opened exciting possibilities for constructing computational simulations designed to replicate human behavior accurately.Current research suggests that LLM-based agents become increasingly human-like in their performance, sparking interest in using these AI agents as substitutes for human participants in behavioral studies.However, LLMs are complex statistical learners without straightforward deductive rules, making them prone to unexpected behaviors.Hence, it is crucial to study and pinpoint the key behavioral distinctions between humans and LLM-based agents.In this study, we highlight the limitations of LLMs in simulating human interactions, particularly focusing on LLMs' ability to simulate political debates on topics that are important aspects of people's day-to-day lives and decision-making processes.Our findings indicate a tendency for LLM agents to conform to the model's inherent social biases despite being directed to debate from certain political perspectives.This tendency results in behavioral patterns that seem to deviate from well-established social dynamics among humans.We reinforce these observations using an automatic self-fine-tuning method, which enables us to manipulate the biases within the LLM and demonstrate that agents subsequently align with the altered biases.These results underscore the need for further research to develop methods that help agents overcome these biases, a critical step toward creating more realistic simulations.