Painting - Paint peeling

I have an older home, the paint is peeling in a few places. On the ceiling on one room and on the wall in another. I know that the previous owner used oil base on some of the areas. I have been told that the top coat was not letting the under coats "breath" and that is what is causing the peeling. Is this true and will the rest of it peel off eventually? Do I have to remove all the coats down to the bare wall and then paint? What is the best way to remove the old paint?

It is hard to give you an answer from the info that you give. It could be that it is latex paint that was applied over an oil base paint and the latex is peeling. Or , is there any possibility that water could be getting behind your walls? If you are lucky, you may be able to sand as much as you can off, and then prime your walls with a good oil based primer, if the peeling was bad, you then mudd the spots that would not sand smooth, sand them smooth and then prime those spots. And then you sand the entire area again. Now you are ready to paint. good luck.

I have been told that the top coat was not letting the under coats "breath"
Never heard of such a thing, except for some rare exterior applications, or new, uncured plaster.
Remove/sand off just the failing layers, down to a stable surface. Then prime with an alkyd or oil primer. This will allow you to do repairs and repaint with any product you want, latex or oil. Choose latex, oils are being pushed out of the industry due to VOC regulations.