How do I correct peeling of white cabinets?

You could stand them down and then repaint them. If you use a chalk paint, you just have to sand down the worst of it, clean it, and then paint it. Chalk paint can self level and it's easy to work with.

If you're going to the bother of removing cabinet faces, sanding to bare wood, and repainting, use a long lasting primer and paint with a paint sprayer or excellent brushes and rollers, followed by a top grade sealer. Ask the paint department personnel in a specialized paint shop about the longevity of their paints, used in a kitchen.

Take a cabinet door or drawer (or a good photo if that’s all you can take) to the paint department of the home improvement store and ask them what will work for you. They have the best selection, the most up-to-date materials and most important, the most informative sales staff to get you what you need for a professional job and can help figure out what is going on.

Thank you for your help