While refinishing a wood floor, I put masking tape around the room to keep the varnish off the wall. Pulling off the tape caused this to occur everywhere.

Someone had painted latex paint (acrylic - lean) over some old oil-based (fat) paint, which is also notorious for this problem.
Comments
Try this:
Professional premium-quality low-tack masking tape specifically designed for a crisp, sharp line on delicate surfaces such as freshly painted or plastered walls, wallpaper, treated wood or emulsion paint. UV resistance allows for clean removal after long exposure to sunlight.
As discussed elsewhere here a heat gun or hairdryer will soften the adhesive to allow easy removal.
Denis