I would say that you were old enough for responsibility. I was never allowed them at home, but when I moved out I got my animals.

I think the best way would be to do more stuff round the house, and show her that you have responsibility. She isn't going to want to be whined at because that will probably make her more inclined to say no. Accept that she says no, and don't sulk, and just show that you are responsible. She is probably going on past experience, but now as you have grown up, you are different. If you show that you have grown up, and don't act like a child about it, she may be more inclined to say yes.

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