I think I should clear this up because this is one of the MOST COMMON misconceptions in the painting business.
Latex primers and paints in North America are primarily made from one of two kinds of plastics;
A. polyvinyl acetate, which you probably know better as white wood glue, and
B. polymethyl methacrylate, which you probably know better as Plexiglas.
Generally, budget priced paints and general purpose primers are made from polyvinyl acetate. In the paint industry, primers that use polyvinyl acetate resins as the binder are called "PVA" primers, whereas paints that use polyvinyl acetate resins as the binder are called "Vinyl Acrylic" paints.
Top quality interior and exterior latex paints and fresh concrete primers use polymethyl methacrylate resins as the binder. The wording "100% Acrylic" on a can of paint simply means that the binder resins in it are made of polymethyl methacrylate.
Polymethyl methacrylate resin binders are better at most qualities that make for a good paint except being cheap to buy. The three biggest differences are that:
1. Adhesion is something that's just hard to engineer out of the white wood glue (polyvinyl acetate) molecule, and so primers and paints that use a polyvinyl acetate resin binder will be slightly sticky even when fully dried. The characteristic is called "blocking" and PVA binders are said to have "poor blocking resistance" because dry PVA paints will tend to stick to each other. PMMA (polymethyl methacrylate) primers and paints have good blocking resistance because the dry plexiglas film won't be sticky at all.
2. PMMA (polymethyl methacrylate) primers and paints will stick much better when applied to moist or damp surfaces, and...
3. PMMA primers and paints are much more resistant to water and damp or moist conditions. Budget priced paints that use a polyvinyl acetate resin binder will both soften and lose their adhesion in moist, humid or damp conditions, or when they're directly exposed to rain or water. The result is that the PVA paint film will soon crack up and peel off, and this is commonly misdiagnosed as being due to poor prep work prior to painting.
If a 100% Acrylic paint was used, and you see the paint peeling EVERYWHERE in the bathroom, then there may be reason to believe the problem was poor prep work prior to painting. However, if the peeling is restriced to the upper walls and ceiling of the bathroom, especially the ceiling over the shower area, then there's no question that the problem was the kind of paint used, not the prep work. This is because warm air will both rise and contain the most amount of moisture, so the problems associated with PVA's poor moisture resistance will first show themselves in the moistest areas, which are at the top of the room, and closest to the source of moisture.
If this happens to you, it is NOT necessary to remove the old PVA paint. Simply scrape off any loose PVA paint, skim coat with joint compound to restore the smooth flat surface of the wall or ceiling, prime with any latex or oil based primer and then paint over the old PVA paint with a PMMA paint. The PMMA paint will prevent the PVA paint from getting wet enough to crack and peel.
And, truth be told, it's always best to buy a paint specifically made for bathrooms, like Zinsser's PermaWhite Bathroom paint. That way, not only will you be getting a PMMA resin binder, you'll be getting a PMMA resin that was chosen to be used for bathroom paints because it was more moisture resistant than other PMMA resins. So, you'll be getting a paint that was formulated specifically to be as moisture resistant as possible.
Hope this helps.