Ok, I have the answer.
Chasing pigeons is a normal thing for an inquistive child to try. But I think a responsible parent should then say 'Tarquin, darling, be kind to the pigeons, don't scare them'.
Thus teaching respect to animals and weaker beings.
If parent says 'haha, look, the pigeons were really scared when you did that' then they are teaching that it is fun to scare animals and weaker beings (in which I incldue smaller/vulnerable children).
If a child learns to respect insects/birds/fish etc then they will learn to respect each other. If the message is given that 'it's just a pigeon' then they will have no respect for animals/people weaker than themselves.
I'm sure a pigeon isn't really traumatised by a child chasing it. But the child may grow up that little bit less caring and respectful, and may grow to really harm things or people.
As I said earlier, my children rescue insects and snails, and rather than saying 'FFS' as one poster kindly put it, I applaud them for their care for the world about them.