Your not putting oil based paint on latex are you? This does happen like this on cheaper paints.
I would go over the entire surfaces and lightly sand or scrape away any areas that flake away like this. Then feather out the areas where the paint makes the boundary. If the boundary lines are thick, then you may have to float in that area.
Then go over and re prime the entire area. Make sure the surfaces are clean and free from any grease, grime or chipping. Apply a good quality paint product from a Paint Dealer. Let all the coats dry properly and don't rush it.
You should be on the right track. Sounds like the moisture in the new paint is soaking through the old paint and causing the release, just like painting over wall papering if the paper is actually paper.