Descartes' method of deconstruction depended upon the fact that he could
doubt something; he could doubt that the past was accurate, he could doubt his logical abilities. The only thing he could not doubt was
thought itself - for even doubt of thought was thought.
However, this hinges upon the existence of doubt! Since doubt is a type of thought, his argument is circular, and therefore flawed.
What he was actually doing was first assuming the existence of thought, then going on to show that this 'proved' thought, and therefore himself, to exist.