It was never sanded properly, nor cleaned properly or primered with a good quality bonding primer before painting. Only thing that can be done now, is to take them down, and sand like crazy, clean them with a good cleaning product, and then wipe them down with tack cloths, and put a good coat of bonding primer on, and finally 2 good coats of quality paint. It will be more work now, to fix them, than it would have took to paint them in the first place.

Are these real wood doors or vinyl or fiberglass ones?

Since you're saying that the paint is pealing really easily, you may be able to scrub & peel most of the rest of paint off.

Peel the paint off, sand lightly, and prime with a quality primer. Then paint with a high quality paint. That;s what I had to do with a door at my mothers house.

Those look like plastic doors.

Know that "remove existing paint, then prep properly and repaint" is the right answer, replacing the doors is probably easier and will get better results in the end.

Another vote here that those are plastic (or fiberglass) doors. Using chemicals or sanding to remove the existing paint may be complicated. Decent new wood doors for closets aren't that expensive, would look better, and might be less of a hassle.