A family of Microsoft word processing software products for creating web, email, and print documents.
To delete the header on the first page, you have to select "Different first page" on the Header & Footer Tools Design tab (which you'll see if you first double-click the header to activate it). The option creates a separate header, and a separate footer, for the first page.
With "Different first page" selected, the current section has two headers (and two footers). You can have up to three types of headers (footers) in each section, which is the case if you also select "Different odd and even" on the Header & Footer Tools Design tab.
If you want to change header and/or footer content on subsequent pages, you have to insert section breaks (Page Layout tab | Breaks | Next Page) and then click to deselect Link to Previous on the Header & Footer Tools Design tab. Note that each type of header, and each type of footer, must be separately unlinked from its "neighbor" in the preceding section.