If the undercoat comes off easily, you haven't prepared the surface of the door properly. The surface to be painted has to be cleaned of any grease and dirt using sugar soap. Clean off with clean water and let it dry. Rub the surface down with fine sandpaper or wet & dry to get a key for the undercoat to adhere to. Wash & dry again then wipe down with a rag soaked with white spirit or turps to remove any dust left on the surface. Now you can apply the undercoat, let it dry, and then lightly sand and clean it as before, if it needs another undercoat repeat as before, then the topcoat can be applied. It takes time, but the more effort put into the preparation, the better and longer lasting the finish.
Mr Dulux, December 2009