Matt Ridley makes a few good points, I think.
It turns out that the great majority of this energy, 10.2% out of the 13.8% share, comes from biomass, mainly wood (often transformed into charcoal) and dung. Most of the rest is hydro; less than 0.5% of the world's energy comes from wind, tide, wave, solar and geothermal put together. Wood and dung are indeed renewable, in the sense that they reappear as fast as you use them. Or do they? It depends on how fast you use them.
One of the greatest threats to rain forests is the cutting of wood for fuel by impoverished people. Haiti meets about 60% of its energy needs with charcoal produced from forests. Even bakeries, laundries, sugar refineries and rum distilleries run on the stuff. Full marks to renewable Haiti, the harbinger of a sustainable future! Or maybe not: Haiti has felled 98% of its tree cover and counting; it's an ecological disaster compared with its fossil-fuel burning neighbor, the Dominican Republic, whose forest cover is 41% and stable. Haitians are now burning tree roots to make charcoal.
You can likewise question the green and clean credentials of other renewables. The wind may never stop blowing, but the wind industry depends on steel, concrete and rare-earth metals (for the turbine magnets), none of which are renewable. Wind generates 0.2% of the world's energy at present. Assuming that energy needs double in coming decades, we would have to build 100 times as many wind farms as we have today just to get to a paltry 10% from wind. We'd run out of non-renewable places to put them.