As you were already told here and on your question to the German branch, pages do not exist in the document. They are artifact of processing of the document by software.
Specifically, a document is data and rules how to layout the data (pagination rules are among them). In the document, there’s nothing like “Page 1. Start at (x1,y1) and output the symbols ABC. Go to (x2,y2) and output symbols …” etc. There are paragraphs/text runs with text and their properties, and those properties tell what formatting rules to apply; some paragraphs have special property “start me from new page (possibly with page style XYZ)”. First paragraph implicitly has that property. Other paragraphs (not the first, and not those that have that property) may or may not start from new page in the result, and may split over page break - the document itself doesn’t know that.
LibreOffice knows that (it does the actual layout, and positions portions of text to specific places on created on-demand pages); but even it cannot create you a document that is single “page 2” of initial document. That is non-trivial task. Consider just two cases:
- A paragraph is split over the 1st and 2nd pages. It has a first-line indent, and space before it. Its first 3 lines are at the end of page 1, and last 4 lines are on page 2. Of course, its line 4 (the first on page 2) has no special indent, nor space before (because they are on p.1 applied to 1st line of paragraph). But if you extract the page and make the 4th line the new 1st line of new 1st paragraph of one-page document, then how should it be formatted? It has its paragraph style (or direct formatting) that tells it to be formatted with indent and space before - so will the formatting be skewed? Or should formatting be changed somehow to create visually the same picture - but then the document will behave differently from the original, i.e. it will be not the 2nd page of original, but something that resembles that?
- A page has headers with chapter name on it. You have a middle page of a chapter, and try to extract it to one-page document. But in this new document, there’s no chapter heading, which would allow the header’s field to get its data. So, once again, either formatting is lost, or internal data is absolutely different from what was on the original page of original document.
In both cases (and in any other case that has similar problems), if you opt for “give me the file that is visually identical to original, no matter what the internal structure is”, then you are actually seeking for a fixed representation that has its dedicated format. That format is called PDF, and you can create PDFs of any document, and split it to single pages that look identically to original, using tools like ghostscript, PDFill and many others. So, please use that.