Is it your paint that peeled off, or the paint that was applied at the factory?

My Paint...on top of the factory paint.

It could be that the factory paint was not compatible with your paint, although I have had blue tape pull off paint before too. I rarely use blue tape for that reason and because it almost always allows leaks under it. Besides, I get a better line just using an angled brush. If you do get it sanded down, you should prime it before you paint.

How about putting wall paper there instead?
Diane

I'm guessing that you didn't prep the factory paint before you painted latex over it. If the factory paint was oil based, latex won't stick to that unless you prime with an oil based primer first. Oh, and you'd need to scuff the factory paint up with sandpaper before you prime.

You need to take the tape off before the paint dries, or the paint will "bridge" between the the tape and the surface that you painted. It is sticking to both the tape and the surface and the paint doesn't "know" where the edge of the tape is. (I hope that makes sense) If the paint does dry completely you can cut along the edge of the tape with a razor to get a clean paint edge.

Unless it is latex over oil paint, then it is probably the prep. Did you wash and/or possibly sand the surface you want to paint? If there is dirt/dust/grime, the paint will not adhere.

I will bet everything that your factory paint is oil-based and latex over oil will peel if not primed first. We had that happen with a professional painter on closet doors. We called another painter in and he said that is what the problem was. I think a factory would use oil, not latex.

so what do I do to fix it? Will sanding do the trick...or do I have to completely removed (strip) the latex paint off...and, of course, that would more than likely strip the factory paint job off too. It's a brand spanking new cabinet...no dust or dirt had built up. it has never been used...so I guess it's the latex over oil problem. I'd a ppreciate some advice on what to do now to remedy the situation.

Storklady---I hate to tell you this...but you are going to have to get that latex paint off. You may not have to resort to chemical strippers. Try using a plastic scraper and see if you can get the latex off without resorting to chemicals. If not...get ready to strip.

Check the rest of the new paint and see if it adheres well. If so, you can give it a light sanding and level it out with some light drywall compound or Bondo. Apply a couple of coats undercoat, sanding after each coat dries till you get a smooth surface. Then apply the finish coat. Always take off the tape before the paint dries like Terriks says. If the paint you put on peels off, then peel and scrape off as much as you can, sand, and apply several coats of good undercoat sanding between each coat, until the surface is smooth with no brush marks or pits. Then apply the finish coat. If I were you, I would try a different brand of paint. Or not.

Yikes! It's peeling because there was literally nothing for the paint to stick to, except for the tape, that is. Before you paint any slick surface, you should at least give it a good sanding, (known as giving it a tooth) and then prime. Also, you shouldn't use latex over an oil paint. But, none of that matters now.
You can A). completely sand the surface, prime and then paint again. Or, B). have a panel cut to fit; 1/8" beadboard or MDF, then prime & paint the new surface, trim out top, bottom and 2 sides with a small profile moulding. Make sure your shelves will fit w/the moulding, or you can simply use caulk if there is a gap.
(I also posted this on the paint forum, but thought I'd put it here, too)
I hope this helps, and I do love the look of a contrasting color on cabinets.

thanks everyone for your help. I figured I'd have to either sand or strip and start from scratch. I don't mind as I want it to look good...that was the whole point of painting it. ha. I always sand before I paint. I feel so stupid. I just didn't think it ws necessary on a brand new cabinet and I didn't think about the finish being oil based. I think I'm on overload....there has been So much to do and SO much work involved and we are in the home stretch and I'm SICK TO DEATH of the mess and I just didn't think last night at 9 p.m. when I decided to tackle the job. Dumb. Dumb. Dumb. Thanks again.