Painting over cabinet doors

I think it depends on the quality of the old paint? any chips, cracks, peeling? then you might want to sand a bit to make sure you have a smooth surface to start. I would probably sand and clean a bit anyway to give the new paint a better chance of adhering.

If the previous paint was done in thin coats and your cabinet doors are smooth you could probably paint over them. If the paint is old and thick looking with peeling areas try to sand it all down to a smooth finish--making sure any paint in any decorative grooves is removed well. You won't have to get all the paint off in the grain of the wood--just get a smoother satiny like finish. Then wash well, dry well, prime, and repaint. You could strip them but that is a huge job. It may take a while with lots of patience so don't plan to be done in a weekend.

you have to remove old paint

for the paint to properly adhere, remove and start over.Use Citristrip a safe non-toxic paint remover