why don't carbons use sp3 instead of sp2 orbitals to make double bonds?
Only one electron can be in an orbital at a time. There are three p orbitals, one in each of the x, y, and z axes. A pi bond is the overlap of one p oribital from each atom. Like the p orbital, a pi bond also can be rotated from the x axis to the y or z to produce a different unique pi bond. Because a sigma bond has rotational symmetry, rotating it does not give a unique bond. Therefore, you cannot have two of them between the same pair of atoms.

Edit: It appears this question has been asked before and there are much better answers than mine (Why can there not be more than one sigma bond in a set of bonds?)