Quoted from RC_like_the_cola:The tape pulled up the paint because it wasn't bonded to the wood trim. Looks kinda glossy, so I imagine sanding the trim lightly to give the paint something to bite to will stop it from lifting. The other option is don't use tape on the next room. I personally never tape when painting. I always had issues with paint bleeding under the tape or something, so I just practiced and got good at edging freehand.
Aren't you supposed to pull the tape while the paint is still wet to avoid pulling like this too?