So I use a screenshot capture program to capture a part of the screen and copy it to the clipboard.
Whenever I paste it into Illustrator, the captured object is automatically resized to smaller and thus pixelated (zoom level always at 100%). It only becomes clearer when I make it bigger.
This doesn't happen when I use the built-in Print Screen function of Windows or when I paste it into Windows Paint or Photoshop. Also, it is the same with two different popular capture programs (SnagIt and Greenshot) so I suspect it comes from Illustrator.