The requirements elicitation process often starts with an interview between a customer and a requirements analyst. During these interviews, ambiguities in the dialogic discourse may reveal the presence of tacit knowledge that needs to be made explicit. It is therefore important to understand the nature of ambiguities in interviews and to provide analysts with cognitive tools to identify and alleviate ambiguities. Ambiguities perceived by analysts are sometimes triggered by specific categories of terms used by the customer such as pronouns, quantifiers, and vague or under-specified terms. However, many of the ambiguities that arise in practice cannot be rooted in single terms. Rather, entire fragments of speech and their relation to the mental state of the analyst need to be considered. In this paper, we show that particular types of ambiguities can be characterised by means of argumentation theory. Argumentation is the study of how conclusions can be reached through logical reasoning. In an argumentation theory, statements are represented as arguments, and conflict relations among statements are represented as attacks. Based on a set of ambiguous fragments extracted from interviews, we define a model of the mental state of the analyst during an interview and translate it into an argumentation theory. Then, we show that many of the ambiguities can be characterized in terms of 'attacks' on arguments. The main novelty of this work is in addressing the problem of explaining fragment-level ambiguities in requirements elicitation interviews through the formal modeling of the analyst's mental model using argumentation theory. Our contribution provides a data-grounded, theoretical basis to have a more complete understanding of the ambiguity phenomenon, and lays the foundations to design intelligent computer-based agents that are able to automatically identify ambiguities.