Mainly transformer has high inductance and low resistance. In case of DC supply there is no inductance ,only resistance will act in the electrical circuit. So high electrical current will flow through primary side of the transformer. So for this reason coil and insulation will burn out When AC current flow to primary winding it induced alternating flux which also link to secondary winding so secondary current flow in secondary winding according to primary current. Secondary current also induced emf (Back emf) in secondary winding which oppose induced emf of primary winding and thus control primary current also. If DC current apply to Primary winding than alternating flux is not produced so no secondary emf induced in secondary winding so primary current may goes high and burn transformer winding.