Where does ductal carcinoma arise within the breast?

Ductal carcinoma arises within the breast primarily from the cells lining the ducts, specifically in the extralobular terminal ducts. These ducts are part of the lactiferous system and lead from the lobules, where milk is produced, to the nipple. Ductal carcinoma starts in the epithelial cells that can become cancerous due to mutations and other genetic changes.

The choice representing the extralobular terminal duct is correct because this site is where the majority of invasive ductal carcinomas originate, reflecting the tumor's classification. The extralobular terminal ducts serve as a key area in the breast anatomy where the proliferation of abnormal cells can lead to ductal carcinoma, thus making it the appropriate answer.