My parents told me to take care of the fish myself.
Is it your fish? Your parents don't want to help you take care of it any longer?
No, they don't want to take care of my pet.
If the fish is your pet, you're expected to take care of it yourself. You should read up on how to look after your goldfish, it will be more rewarding to provide for it on your own.
I'm mad at them because I don't want to take care of my own fish.
What they are saying makes sense. It is your pet so you bear the responsibility of taking care of it. If you do not want to take care of it, then you should give it to another owner who will.