To see why, let's use the usual reduction of the problem to
packing spherical caps into a sphere, and let's change the size
of these caps to that at which there's room for just 8 mutually
tangent ones, centered at the vertices of a cube.  Then after
starting with two touching ones of these, your method would
place a third so as to touch both of them, which would prevent
it from finding the correct configuration.