Does "remodeled", mean that old cabinets were painted over, or are there new cabinets that are peeling?

I believe old cabinets were painted over.

More than likely improper prep in the normal cause of paint not sticking. Strip and paint over is typically the only remedy. More so the case since it sounds like the paint was slapped on to help sell the house, not improve the kitchen.

Improper prep before painting. Either no primer, or not the right kind of primer, and may not even be correct type of cabinet paint. There is only one way to fix, and thats to strip them all, and sand them all smooth, and all dust removed, and then paint them properly.

Sand to bare wood and start over. Or buy new. There aren’t any half measures for peel in paint on cabinets.