Abnormal cells found in breast cyst aspirate. Cells chunkier than normal. What could cause this?

Your doc must answer. As a pathologist, I use many different words but "chunkier" isn't one that's familiar to me from breast biopsy aspirate work. You have a right to a complete explanation -- any chance of cancer? -- from the pathologist if your primary care physician or whoever did the aspirate cannot answer for you.