I’m not a geologist, but having worked in the construction industry for nearly all of my adult life I have learned a little about abrasives.
Water, by itself, is not a great eroding medium. Pure water, that is. Wind – as moving air – even less so.
It’s the things which those media carry that cause erosion: sand, silt, acids and bases, and even the vegetation carried away, which loosens more soil and exposes more rock. Those hard things cut rock. (And some “rock” is cuttable by water alone, when the rock is a soft sedimentary rock to begin with, such as sandstone and some shales.) Wind, by itself, also doesn’t do a lot to rock. But when high winds carry sand, that’s nature’s sandblaster.
However, to get back to “pure water”: over changes of season and during periods of glaciation, ice is good at breaking and grinding rock. And rocks falling on other rocks – including the scree that forms at the base of many cliffs as they decay with seasonal change and freezing water breaking into fissures of the rock face – that creates the smaller rocks, and sand that flows in rivers to erode rock faces.
And erosion obviously feeds itself, too.
You might say, “But floods are great masses of water, surely they have a cutting action.” And you’d be partially right, but if you look at videos of floods (flash floods, especially), you never see very clean water. It’s the things carried by the water that cause the erosion.