The reason is simple-in my testing, clicking those options removes the header or footer text, but it doesn't remove the header or footer paragraph. You may wonder why you don't just click Remove Header or Remove Footer, options available after you complete step 3 of these steps.

On the Header & Footer (or Design) tab of the ribbon click on Close Header and Footer.

As long as you are actually in the header or footer, only the header or footer contents will be selected.) (A quick way to select the entire header or footer is to press Ctrl+A. Make sure you get all the contents, including the paragraph mark at the end. Select the contents of the header or footer.Word displays the header or footer along with the Header & Footer tab of the ribbon (Design tab in older versions of Word). Click Edit Header or Edit Footer, depending on which tool you clicked in step 3.Word displays a drop-down list of options. In the Header & Footer group, click either Header or Footer, depending on which one you want to delete.

Position the insertion point in the section that has the header you want to delete.

If you want to fully delete a header or footer in your document, follow these steps:

How to insert a save header in word