When you copy this image
and paste it (via drag and drop from Google Chrome) to Libre Office writer (4.3.3.2) you get:
Why is this so pixelate / fuzzy?
Somehow it does not coy the original image. How can I tell it to copy it in the original size by default?
But even after setting it to the original size, it is still pixelate. How can I fix that?
What is the number of pixels? What are the dimensions of the original image?
Your example was surely supplied in a pixel graphics format. Inserted into your ‘Writer’ document it obviously changed size. This will mess up the rendering for pixel graphics.
Possible causes for the resizing: (1) You did it. (2) The size was not correctly deployed during the drag/drop.
I couldn’t test your attached graphics. With examples from the web I often got wrong size with drag/drop while ‘Copy graphics’ (Firefox)/ paste did it well.
Please note that LibreOffice cannot have full control over the drag/drop process. The web publishing software of the supplier, the browser, the drag/drop (or copy/paste) facility of your OS will play their part.