Pushing down on the tailplane could cause damage to the spars as the load is localised. There were incidences of cracks in the rear fuselages of C150's as a result of heavy handed handling of the tail. Take it easy and spread the load and it should be OK.
Props blades close to the hub are OK for pulling and pushing. Cub's have a neat little handle for lifting the tail. Pity other aircraft didn't have something similar to reduce confusion and damage