Is it really impossible to make a div fit its size to its content?

You can use display: inline-block.

You can use:

width: -webkit-fit-content;
height: -webkit-fit-content;
width: -moz-fit-content;
height: -moz-fit-content;

EDIT: No. see http://red-team-design.com/horizontal-centering-using-css-fit-content-value/

ALSO: http://dev.w3.org/csswg/css-box-3/

CSS display setting

It is of course possible - JSFiddle proof of concept where you can see all three possible solutions:

• display: inline-block - this is the one you're not aware of

• position: absolute

• float: left/right