In design the word "modern" has a specific meaning. Modernism is a movement, a school of thought that emerged in the early 20th century with Bauhaus and designers such as Mies van der Rohe who famously said "Less is more". It's a rejection of ornamentation and unnecessary elements. It embraces honesty for the medium and materials, and the idea that "form follows function".
The reason that flat design is modern is because it rejects the use of shadows, bevels, glossy textures because these are decorations that attempt to make a digital interface look like something it is not (i.e. real objects in the real world).
Just to tag along - I was surprised when I first saw early 1920s typographic/graphic design (esp. book covers) just how closely the newer "flat" UIs resemble that period's style.
One could make the argument that Forstall's iOS was post-modern. The choice of using real-word textures such as leather and notepaper were not just about helping novice computer users, they also seemed like an aesthetic choice, decorative features along the lines of Robert Venturi's architecture. I think Forstall might have agreed with him that "less is a bore".
The reason that flat design is modern is because it rejects the use of shadows, bevels, glossy textures because these are decorations that attempt to make a digital interface look like something it is not (i.e. real objects in the real world).