Use lotion. It softens the cuticles so that you can push it up. Cuticle away could damage the nails if you leave it on too long, and it can be difficult to remove.
Be careful with lotion though. If you get it on the entire nail plate it will soften the surface layers, making it easy to scratch the plate. Put the lotion on the cuticle area and sidewalls and then push/nip loose skin tags.