Rear edge of composite props can be fragile
The rear edges on the composite prop on my aircraft are very fine and taper down to maybe 3 mm thick (just about this thin all along the rear edge, even towards the prop root).
I have personally seen these rear edges damaged when pulling on the prop, by a rampie with rings on his fingers, where the rings rolled over the rear edge when pulling - chipped the rear edge in a few places, requiring repair.
Pushing at the root seems ok [where you are pushing on the wide front edge], but having seen this myself I would never pull on a composite prop (and to save misunderstanding I insist that rampies never push or pull on my prop).