Almost without doubt your cabinets have a heat set precat lacquer on
them. They may also have dirt, detergent residue left from an
occasional cleaning, silicones left behind from a dusting agent, and
maybe wax from an attempt to spruce them up.

If it was me, I would start this way:

- Wash them down with a wet, sloppy rag full of lacquer thinner,
changing the rag often

- Sand every surface to be painted, and wash again with the lacquer
thinner. Be careful how you handle the cabinets while you are working
on them as you can leave leave fingerprints of sanding dust (like from
the back where you arent' going to paint, but still have the dust on
them) in the newly washed areas

- Apply a generous coat of Paso, or any other kind of solvent based
liquid sander. It doesn't really sand, but it does etch and will do
some cleaning

- Prime with a SOLVENT based primer like Bullseye sanding sealer.
Your luck with adhesion using the "white stuff" probably won't be that
good as it won't penetrate the wood surface since it was sealed with
the precat

- Paint with a solvent based finish

That should do it. BUT.... to be absolutely sure, you could strip
them and start fresh. If it was only a few cabinets, it should take
long to do that. Strip, sand, prime, paint.

Robert