The page you want to print may have its 'format page number' set to an even integer (when the page should be an odd page) or vice versa. If so, Word will insert a blank page either side to give you what it thinks is the right outcome. The cure is to change
the format page number from even to odd (or vice versa).
To do this (in Word for Mac 2016), click into the header or footer of the page concerned, where the page number is or would be. Then click on the page number icon in the ribbon (under 'header and footer') and choose 'format page numbers' .
In my case I had put a picture on a page by itself with section breaks (i.e. section break: next page) on both sides of it. The section breaks allowed me to remove the page number from the illustrated page, while leaving page numbers either side.
But even though I had removed the page number, Word still 'knew' that the page concerned 'should' be an even page, and inserted blank pages to achieve this outcome--and without showing this in 'print layout' view. I have now changed the format page number
box to '1' (an odd number). Problem solved.
And thank you Microsoft for wasting four or five hours of my time while I found the solution. Instead of changing my document, why didn't you just warn me that the pagination was going to be wrong if I wanted to use it which I didn't?