Fun fact: all cockies are left-handed. I used to live in Canberra, where they're plentiful. I heard this 'fact' and was doubtful. Well, I've since seen hundreds of these birds eating acorns and, can confirm, every one a leftie.
A crab finding itself left-clawed means they fight differently and are generally less successful in fights, thus they live a more asocial life by choice and necessity. https://en.wikipedia.org/wiki/Gelasimus_vomeris
Update: see comment below. Studies are not conclusive.
https://www.psychologytoday.com/us/blog/the-asymmetric-brain...