My guess is that your family loves to fiddle with the cat and bother it whenever it's near them. Hence why it would appreciate you.

You may already know this, but maybe not, so I'll say it...most people that have cat allergies are actually reacting to the dander in their skin. If you keep the house clean, and kitty does a good job of cleaning herself (most cats do), you may find that you don't have a problem. But you've GOT to keep the house clean; that stuff accumulates in every crack and crevice. And, of course, there are medications you can take if you still have a problem.

To clear it up, just beacuse you are allergic to cats doesn't mean you can have one. Myself are allergic to cat but I wouldn't mind getting one either, even I've noticed thick throats and itching/red eyes all the time when visiting all my friends that have cats. I mean, even if I know it will be painful, I can't keep my eyes and face away from those awesome creatures!

Why did your family get a cat knowing you're allergic..?

The cat of the devil?

Stare the cat right in the eyes. Cats take this as a sign of dominance and will tend to avoid you if you do this often.

If OP likes the cat, maybe Benadryl or some other allergy medicine may help.

Damn! That's ****** up!!

I'd have to agree with the "lack of interest" approach if you want a cat to approach you, based on personal experience. When my boyfriend and I started dating, his cat would usually run away when I walked into the apartment (mainly because I was a stranger), and it didn't help that I have a weakness for animals and usually run up to them to pet them or greet them the first chance I get. After the newness of the cat wore off (and the numerous failed attempts to get close to her), I gave up and started to let her mind her business. Sure enough, a day later, she was walking up to me and getting *just* out of arm's reach to tilt her head and stare at me for a few hours, maybe even throw in a few chirps and mews here and there. It took a while to get her to warm up to me, but, nowadays, she won't hesitate to sit in my lap and demand pets if she sees me grabbing a throw pillow on the couch. Cats love to play hard-to-get (probably for body language reasons, as stated in the other comments), so you have to play it right back at them to get any sort of recognition from them.

I don't understand the logic in a family getting a pet that a household member is allergic to.