We've not really had them in the TV series, but Arya has warg dreams where she is Nymeria... I get the impression they're both loners. Predators. I took "That's not you" to mean, "following me around getting tickles under the chin isn't you, you'll do your own thing, but now you know I'm here you'll appear when I need you to... like if I'm about to get eaten by a bunch of your cousins."