Headers are designed to be on every page. They're most often used for things like titles, page counts, etc.
Pages does support sections, where you can define different headers (including blank headers) for given sections, but that option (and the 'Match Previous Section checkbox) only applies if you have multiple sections in your document. If your document contains only one section, then there is no previous section to match, so the option does nothing.
If you have a section of your document where you want different headers, use Insert -> Section Break to mark the beginning of the section, then you can use the Match Previous Section checkbox to toggle the setting.