In recent years, numerous mathematical models of opinion formation have been developed, incorporating diverse interaction mechanisms such as imitation and majority rule. However, limited attention has been given to models grounded in persuasive arguments theory (PAT), which describes how individuals may alter their opinions through the exchange of arguments during discussions. Moreover, analytical investigations of PAT-based models remain sparse. In this study, we propose an analytical model rooted in PAT, demonstrating that a group of agents can exhibit two distinct collective dynamics: quasi-consensus and bipolarization. Specifically, we explore various scenarios characterized by the number of arguments and the degree of homophily, revealing that bipolarization arises within this framework only in the presence of homophily.