how to strip (remove paint) my cabinet doors?

Lightly sand the cabinets and wipe down with TSP. You will need to prime the cabinets first with Kilx-It water based primer. You can have it tinted close to your paint color. Use a good enamel paint for the cabinets....probably a couple coats.

Sand most of it off. The more you're able to get off, the smoother your finish will be. Obviously, wear a respirator. Start with a heavy sandpaper like an 80-100 to get all the shiny stuff off and most of the paint. Move up to about a 220 grit sandpaper and then to a 320. This will cause a nice and smooth finish. Varnish or lacquer is usually put over stained or natural wood, I don't know why you would do this to plywood. But if you decide to paint, do one coat of good water based primer (Zinnser Bulls Eye 123 or a strong all-purpose primer) and two coats of a semi gloss or gloss paint in whatever color you choose. The paint probably scratched off easily because there might've been oil based paint originally on the doors and you put a water based over it or the sheen of any paint or clear coating will keep the paint from properly adhering.

Go buy some paint stripper from the store, and brush it on, and wipe off. good luck, it's a job.

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sand it.. its the only way