[Eomer of the Rohirrim]

Favouritism is not as uncommon as you'd think among parents. There are all sorts of reasons. The Denethor case is particularly interesting because he favoured Boromir over Faramir, even though (and probably because) Boromir was less like Denethor.

I'm not sure whether it's an 'old-fashioned' thing to feel an especial bond with one of your children. Perhaps other Downers with children of their own can give more interesting answers than I ever could.