While fibreglass mesh is relatively hard and resistant to many pests, it’s not intended to be pet proof.
However that really depends on what your pet is like.
Older cats aren't known for shimmying up screening, but kittens are known for their climbing prowess.
Some dogs paw at the screen, while other dogs don't.
If you're worried that your animal will ruin your fly screen, it's possible to buy pet-friendly screening that has been specially hardened.
But remember, there is no such thing as a totally indestructible fly screen.