normally speaking you should be able to paint on top of old paint , rubbing down helps key in the new undercoat, so it could be that, or the old paint was oil based ( the best) the new stuff is water based , for the paint to peel the way it did it sounds like there was grease or oil some were ,
to do the job again remove the peeling stuff , rub down well and paint with a undercoat and top coat that are suitable in combination, if you can find it oil based is best, most paints have gone water based