Because “fair use” is an exclusively a part of the copyright law of the USA and the USA is not a member of the EU.
There are 27 nations in the EU that each have their own copyright law with their own way of dealing with this. For example, German copyright law has a chapter that enumerates specific ways of copying that are permitted without permission (yours isn’t one of them); this is much more like (but not the same) as the fair dealing doctrine used in the copyright law of the UK and other non-US common law countries. You would need to specifically identify which nation’s law applies to the work you wish to copy (by reading the copyright page of the book) and comply with that law.
Yes, it applies to images on websites. Or graffitied on bus shelters. Or tattoos. Or paint on canvas. Or any other way of fixing an image.