Why not continue to encourage her to pat animals but just tell her that she needs to ask Mommy or Daddy first? That way, you can make the assessment as to the "pat-ability" of the animal in question before she puts her little hand near it's teeth! In general, toddlers need to ask permission before they do a lot of things in order to remain safe and appropriate. For instance, they should ask permission before taking food (even if they can reach into the boxes of cereal or cookies themselves, they should ask permission before doing so). They should ask permission to go out of parental earshot or view. They're simply not old or wise enough to make judgment calls on much. Parents can loosen up a bit when they get older for some issues. However, kids should be taught to defer to adult judgment on many issues for a long time (i.e. when is meal time, bed time, bath time, homework time...what activities are permissable & prohibited....it's all up to parents to make many such decisions until the kids are almost teenagers).  Sarah Chana

We told our toddler that some cats and dogs can make an "ouchy" and then she stopped liking any of them and became fearful. So I agree with you to encourage her to continue but just to ask first. No need to scare the little thing! Most pets are tame.

If her vocabulary isn't good just get her to ask "pat?" and you can say yes or no.

I'd rather my child learn to stay away from animals until he's older. Why take risks? Little kids often irritate animals because they don't really know how to pat them properly. When they're 6 or so they're better at it and they can pat them then if they want. I taught my kids to stay away from peoples' pets and they didn't develop phobias. They just accepted it like any other "no" that I told them when they were that age.