Classic diffusely infiltrating lobular carcinoma has imaging features divergent from the breast cancers originating from the terminal ductal lobular units and from the major lactiferous ducts. Although the term “invasive lobular carcinoma” implies a site of origin within the breast lobular epithelium, we were unable to find evidence supporting this assumption. Exceptional excess of fibrous connective tissue and the unique cell architecture combined with the aberrant features at breast imaging suggest that this breast malignancy has not originated from cells lining the breast ducts and lobules. The only remaining relevant component of the fibroglandular tissue is the mesenchyme. The cells freshly isolated and cultured from diffusely infiltrating lobular carcinoma cases contained epithelial–mesenchymal hybrid cells with both epithelial and mesenchymal properties. The radiologic and histopathologic features of the tumours and expression of the mesenchymal stem cell positive markers CD73, CD90, and CD105 all suggest development in the direction of mesenchymal transition. These hybrid cells have tumour-initiating potential and have been shown to have poor prognosis and resistance to therapy targeted for malignancies of breast epithelial origin. Our work emphasizes the need for new approaches to the diagnosis and therapy of this highly fatal breast cancer subtype.