The cytodiagnosis of breast cancer by means of the FNAB technique is the most common confirmatory method used in the United Kingdom for this purpose. Medical doctors have to spend 5 years as a minimum in a training process to become independent pathologists. This fact gives an indication of the complexity of such process: the correct interpretation of cytological features that leads to an accurate diagnosis. Based on this fact, it is natural to think if it is possible to offer computational tools that have the potential for helping cytopathologists in two ways: (a) to accelerate the training process of learning by providing guidance to the trainee on what features are the most important ones to look at, and (b) to compare the final results to those of the trainee or even of the expert so that the decision (whether the sample taken indicates a benign or a malignant output) can be made on a more robust criteria (qualitative and quantitative). The first step we took in achieving these goals was to analyze a pair of databases that contained the diagnoses made by a single observer and multiple observers using the BN framework and check whether this approach was suitable for building accurate classifiers. The results suggest that there is an intrinsic impossibility of building accurate classifiers because of a significant limitation: the well-known interobserver variability problem. That is to say, an ingredient of subjectivity is always present when different observers analyze breast lesion samples. This subjectivity is made explicit using the BN approach, as the results in the experiments carried out here show. A surprising observation is that all the observers made correct diagnoses in all the cases (as confirmed by different methods). However, when we analyzed the multiple observer database, we found that the values they filled in for the independent variables do not allow to build accurate classifiers; i.e., these data are not enough for accurately telling malignant samples from benign ones. These results strongly suggest that the observers are taking into account more information than that contained in the data; a situation that prevents classifiers from performing well enough. Thus, the results provided by the BN framework allowed us to identify that, in order to correctly diagnose breast cancer from cytological data, more information is needed. We argue that0 such finding sheds some light about how the diagnoses are made and may provide new knowledge about the phenomenon under study.