Why is it advised not to use web fonts for printed articles (using LaTeX)? What is the problem in using them?
I'm assuming here that by "web fonts", you mean "fonts developed by Microsoft for web use with low-resolution display devices (~72 dpi)". Fonts such as Verdana.
Verdana is a sans-serif font. The serifs would smudge the shapes at low-resolutions instead of guiding the eye on higher resolutions.
But we are heading towards high-resolution displays with, for example, Apple's Retina displays reaching laser printer comparable resolutions of >300 dpi.
So it would be better today to forget fonts like Verdana for body text.
Also you might be interested to read this: http://www.smashingmagazine.com/2012/04/24/a-closer-look-at-font-rendering/