Can we own a bird pet which will in a cage?

My cousin asked me to get one for her but I said : **"Sorry, It's not allowed in Buddhism and we should care for them not in a cage even if cage were made of gold and must set them free and liberate them"**. So may I know if it's allowed or not? Instead of bad karma I felt myself pity and sorrowful for them. I felt so bad for animals if they're in trouble or something like this. And isn't it same as slavery? We making it as pet for our entertainment and not for caring for them. So please guide me.