Acrylics

No but did you put a coat of primer on before painting? Did you soak all plastic pieces in gentle soap and let dry? Methinks, you didn't and simply painted on top of bare plastic.

I agree with Black Sheep, could be caused by a few things. A good cleaning with mild dish soap and lots of water rinsing helps, a wipe down with alcohol and clean pads also helps.

A good coat of primer before paint allows for good adhesion before paint, also handling of the model deposits skin oils that should be removed. For paint my primer choice is Badger's Stynylrez, (yeah, I know it's a weird name, but it works so well.) Tamiya spray can primer is another winner, but lacks the precision of airbrush application and is a bit pricey.

As good as acrylic is, it does require good surface preparation or it doesn't bond that well.

Patrick

If you can scratch the paint off I suspect there was residue on the plastic. Washing plstic kits is becoming more of a requirement in recent years. Buy the cheap pink dish soap and use it to make soapy water and wipe down the kit on the sprues with it or let the sprues soak over night. If its is still oily or its still doesn't feel clean wipe it down with isopropyl alcohol. In extreem cases you may need to wash it with denatured alcohol. use the denatured outside or in a garage. then rinse it off with water.  Some brands use an ejector fluid or they use fillers in the polystyrene. I'm thinking you bought a F4U in a kit that came with little bottles of acrylic; as I did so last year, and the built kit is in the garage collecting dust because the paint started doing strange things as it dried. I then attempted to fix it and ruined it instead. 

Nah, it was the paints. Testors acrylics are not very scratch resistant, and their adhesion tends to be weak to unprimed plastic. Even with preperation of the plastic, and after the paint has dried and cured. 

Yes Humbrol makes acrylic paints, but I have never used them so I can not comment one way or the other about their quality.