Is this the result of breeding for personalities?
Obviously there are still some wild personality types among domesticated animals but why can only certain animals be domesticated.
If someone could explain the process clearly I would appreciate it.
It’s probably some part breeding, but I think mostly it’s just socialization. House cats that are not raised with humans become "feral" – that is, violently opposed to human contact, just like any wild animal. Similarly with wild dogs (notably dingoes in australia); socialization is responsible for keeping them in line, but without human influence they will revert to their primitive state.
As for why only certain animals can be domesticated – it depends on whether there is a quality of the animal that can be exploited to make them tame and tolerate human presence and touch. Dogs have a pack structure where humans can replace the leader; cats will trade their independence for food and warmth. In other cases (say, crocodiles) where the animal lacks the capacity to make these kinds of bargains, domestication is not possible.