It sounds to me that you’re a great kid, a teenager who has a good head on her shoulders and one who would be able to look at an issue from different perspectives.
First of all, let me congratulate you on earning straight A’s; this is a huge achievement, one that requires a strong motivation. Yes, getting something in return (i.e., a gift, a break from chores, or, in your case, a cat) may be a temporary form of motivation, but the real motivation is the pride you probably feel at achieving something that not many students can ever achieve and the understanding that you doing well in school is for you, for your future success (yes, yes, having a teenage daughter myself, I know that you probably don’t like being lectured to, but bear with me for a bit longer).
Sometimes to avoid such lectures from grownups, teens make their peers their priority; they talk with each other for hours on any and all topics, trade clothes, have sleepovers, share similar interests, etc. I get it. But what I also get, and so should you (yes, the parental voice is creeping in…), is that you have obligations to your family. Let’s say you got your way (as most teens expect) and brought a cat home. Let’s say that your dad got sick, I mean really sick. Let’s play a game: I’d like you to close your eyes and take a moment to imagine your dad being sick because of the new cat in the house. So, you got your way and your dad got sick. Not cool, right?
What’s also not so cool, for you at least, is that you made a deal with your mom and while you lived up to your end of it, it seems that your mom is unable to live up to hers. Yes, your mom should have found out about your dad’s allergies before making that promise to you, it’s her bad, but parents make mistakes too. Simple as that.
Good parents, however, try to rectify their mistakes. The way I see it, you deserve something for living up to your end of the bargain. What about getting a different type of pet? Why don’t you take a piece of paper and pen and list all the qualities you like in a cat? Now think about other house pets that have most of these qualities. Once you come up with another pet of your liking, share this news with your parents. This exercise would truly demonstrate responsibility as a family.