Why are zinc and Scandium not transition metals?

A transition metal is defined as an element that forms a stable ion with incompletely filled d orbitals. Scandium forms a 3+ ion with no electrons in its d orbitals and zinc forms a 3+ ion with completely filled d orbitals. The electronic configuration of Scandium= 1s2, 2s2 2p6, 3s2, 3p6, 3d1, 4s2. When scandium forms its 3+ ion, it loses the 4s2 and the 3d1 electrons to have the configuration 1s2, 2s2, 2p6, 3s2, 3p6. The electronic configuration of zinc = 1s2, 2s2, 2p6, 3s2, 3p6, 3d10, 4s2. Even though the electrons fill up the 4s shell before the 3d, they also lose electrons from the 4s shell first and so when zinc forms its 2+ ion, the electron configuration is 1s2, 2s2, 2p6, 3s2, 3p6, 3d10. Hence, both these electrons form stable ions (SC3+ and ZN2+) with completely filled d orbitals and so cannot be transition metals.