A Poll Investigating the Level of Public Support for Proposed $\pm 5 \%$

Essay

A poll investigating the level of public support for proposed gun control legislation reported that 68% of the respondents were in favor. The pollsters reported a sampling error of $\pm 5 \%$ %. When the responses were broken down by gender, support was 3% higher among women than men. The pollsters said the margin of error for this difference was $\pm$ 6%. Why is the margin of error larger for the difference in support between the genders than for the overall level of support?