Also, clear icons are easier to construct with simple shapes than with detailed pictures, and symbolic icons may localize better. For example, a highly detailed picture of a mailbox varies between a lot of countries; a symbol of an envelope may not, and it's probably more obvious anyway.
Personally, I think a nice middle ground was the original iOS, where you could do cool things like define simple shapes for tab-view icons but have the OS stylize them for you (i.e. a plain white shape would end up with a cool blue gradient and look perfect in the black gradient tab bar, even though the original icon had no gradients or colors or rounded corners). And the UI elements, while sometimes a bit complex, managed to scale just fine between the screen sizes of the time.
I think a lot of people on the flat design bandwagon try to create a false dichotomy with skeuomorphism and try to use this as an excuse. All too often, I suspect they really prefer flat design for other reasons, such as not being any good at more sophisticated styling but also not wanting to hire a digital artist onto a project team, or wanting to avoid anything where the implementation requires real graphics instead of whatever severely limited tools are available using nothing but CSS and the icon font from their favourite UI toolkit. I'm not saying no flat design has ever been done well, but all too often I think it's just lazy and/or unskilled design and the anti-skeuomorphism dogma gets wheeled out to try to justify it in some more flattering way.