A man was fatally shot during an argument with a woman inside a South Chicago home Saturday, police said.The man, 51, was arguing with a woman inside a home in the 8600 block of South Muskegon Avenue about 4:15 p.m. when the argument turned physical, and the woman pulled out a gun and fired shots, according to Chicago police.The man was taken to University of Chicago Medical Center with a gunshot wound to the head. He was pronounced dead at the hospital.The woman was taken to Trinity Hospital and expected to be taken into custody, police said. Detectives are investigating.