My little sister bought a dog yesterday. But since keeping pets is not my thing (I'm too scared of them), I havent been even able to bring myself to touch or pat it. So what should I say? That I'm not a pet person?
If you're frightened of dogs, I would recommend you say that and not say "I'm not a dog person." Saying that you're not a dog person implies that you just dislike dogs for some reason. A dog owner might try to change your feelings by getting you to engage with their dog, because they can't imagine anyone disliking the pet that they find so appealing. If you say "I'm scared of dogs.", most dog owners will understand that is not something that you can easily change your mind about, even if their pet is a really nice dog.
Here's another example: if my friend and I are talking about food and I say "I'm not a shrimp person.", my friend might say "Oh that's just because you've never tasted MY shrimp recipe that everyone says is really good! I'll make some for you tomorrow." If I had said "I'm allergic to shrimp.", my friend might say "Oh that's too bad - I have a really great recipe for shrimp. Maybe I'll try it with chicken next time so you can taste it."
When you tell someone that you don't like something that they themselves like, it's just human nature to try to persuade you over to their point of view.
I think people would tend to say "I'm not an animal person" more than they would say "I'm not a pet person." If you are scared of pets, you are probably scared of animals in general.
In this case, I would probably say either that you're not a dog person or that you're scared of dogs. From personal experience, no matter what you say, the other person will try to convince you that their dog is different from all those other dogs out there.