I'm with Rain here. Actually, I was the kid who had a ton of pets, as long as I discussed in carefully with my parents first and got their okay. The whole "Look what I found" or "My friend is giving it away" Well, in my house my mom looked that little orange kitten right in the face and told me to take it back, and she told me to take the snake I'd found outside and kill it [I took it out and let it go instead].
Of course, that all ended when I turned 13 and my parents decided to go back to college, and we lived in campus housing. Which meant that I wasn't allowed to have pets. At all. In fact, most colleges require freshmen to live on campus for the first year, and very few campus's allow students to have a pet, especially the freshmen students, since there are plenty of upperclassmen who want the housing where pets are allowed. That alone is a wonderful reason for the OP's parents to say no to her getting a cat.