The main issue is that you are mixing measurement systems:
ISO 216 specifies international standard (ISO) paper sizes used in most countries in the world today... The standard defines the "A" and "B" series of paper sizes, including A4, the most commonly available paper size worldwide.
In digital imaging, a pixel or picture element is a physical point in a raster image, or the smallest addressable element in an all points addressable display device; so it is the smallest controllable element of a picture represented on the screen.
In these two extracts from the definition of Wikipedia it's clear that one of the measures is for use on paper and the other on device screens. One in millimeters, decimal metric system and the other in pixels, element unit on screen.
If you want to send a document to print, you will choose an ISO format, Din A4 for example and you will use points or millimeters to measure the inner elements. While if you want to create a screen document, the format will be defined in pixels and the size of the internal elements as well.
Explained in another way, imagine you send a 800 x 600 pixels file to print, do you have any idea what paper size it will be?