I know that some women have arm swelling after breast cancer surgery. why?

Lymphedema: The arm swelling you are describing occurs secondary to disruption of the lymphatic circulation draining the arm, either via lymph node removal and/or radiation therapy. When we used to remove 10-20 lymph nodes, the lifetime incidence was ~25%. Nowadays, with sentinel lymph node biopsy alone, the risk is closer to 5%. Hopefully, in the future we won't have to remove any lymph nodes.