The categories of overweight and obese are based on BMI, which is not relative proportion of body fat. On average, of a man and woman who both have a BMI of 30, the woman will have a higher proportion of body fat.
To make a toy example just to make the reasoning clear: if men’s BMI was distributed as 50% = 20, 50% = 35, and women’s BMI was distributed as 95% = 20, 5% = 35, the average body fat of all men would be higher than the average body fat of all women, even though the average body fat of women BMI=X would be higher than of men BMI=X for all X.