Cloud has always been stronger than he thought he was as a child/ young man. He doesn't recognize his own true strength until after he comes out of the lifestream.

Oh, and everyone in the world (or at least those who are reading this) needs to read FF7 Mythologies, by John Brittenham. A small section of this was quoted by astrognats, but the full article (mine is 21 pages...) is a good overview of the true story of FF7.