Impossible to tell from a picture, but many old (75 years or more) plaster ceilings were finished with calcimine - a mixture of glue, water and a white colorant such as zinc oxide. After a time it does tend to peel off bit by bit such as the picture shows even if it's been repeatedly painted.

quote"This house has plaster or sheetrock"

It would really help to know if it is one or the other.

Moisture it is the most common cause of peeling.

This house was built in 52, it's a ranch. It is plaster board, I found a forum that discussed this problem and the bath is next to the DR, we don't have a bath fan but there is a light up there hanging by the wires, it's unattached from the ceiling so I'm wondering if the steam from the bath goes up there through the hole and creates some condensation and/or moisture that could cause this?

I'm just a home owner but moisture will certainly cause peeling or bubbles, which I just took care of at folks house.Another cause possible could have been the original owner not using primer on that ceiling & just painting it.Feel both bathroom ceiling & wall on DR side & ceiling in DR near bathroom, may feel wet or damp. A hanging light(loose) is dangerous & if there is a hole there can have all sorts of problems, moisture will cause rot, what is up above, upstairs you will have floor problems. Need proper repair in bathroom & put in ceiling light & fan combination with 2 switches so fan doesn't have to be on all the time. Find a friend that is good at electrical if you can't or don't know how to do it & be sure it isn't Mickey-Moused!! Surprised your bathroom walls aren't going!!! You need a professional to tell you how to repair that DR ceiling,(hope 1 comes on to tell you) I had to use sander to get off bubbling paint in area about 15x18 where shower steam made it bubble, then I Spackled & let that dry overnight, sanded, primed & let that dry overnight & gave it 2 coats BM white paint. It looks perfect!! Dad now opens door a little so doesn't get so steamy. Good Luck!

Forget the calcimine idea - too new and it's sheetrock. If everything is peeling right down to the paper on the sheetrock, then the primer has failed or possibly no primer was used. If the paint is peeling off the primer itself, then the paint failed to bond to the primer. There can be many reasons for this. If the peeling is completely confined to this one area, then moisture from the bathroom may well be the culprit. It does, however, seem pretty unlikely that enough moisture to cause peeling could have accumulated here. Moisture trapped above the ceiling would have dampened the sheetrock enough to be visible as a stain before the paint let go. My best guess is that the primer/paint job is at fault.