The Calabi-Yau manifolds do not get compactified to anything. Strings get compactified on Calabi-Yau manifolds. We can choose any type of manifolds to compactify string theory on, for example a circle, a torus, the Klein-bottle and other similar topological spaces. Witten, Strominger, Candellas et al. trying to extract various properties of string theory that should resemble to properties of the four dimensional space-time we are used to along with mathematical consistency and physical properties (such as the number of supersymmetries they preserve) lead them to consider compactifications on CY. Strings by no means "need" to be compactified in four dimensions. CYs provides us a very possible way that the extra dimensions of string theory are "curled up". That's all.