Use a razor blade to cut along the edges of the tape before pulling up.
This problem occurs because people don't utilize the tape the way it was made to be used. It shouldn't be painted on, or slathered with paint. It is just there for mistakes. A careful hand and a good brush should be used to cut in with, and the tape is there for accidental over runs, not as a complete guide for the cut in.
The fact that the paint is peeling off is also an indication of an adhesion problem. The trim/walls weren't prepped correctly, most likely weren't sanded enough to provide good 'tooth' for the new paint to grab onto.
To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.