Why does my mum always do the things i tell her not to do (always have a reason)?

It is her responsibility to parent, not yours. Perhaps trying a different approach and 1) Nicely explain why the door needs to stay open and ask if she has any suggestions to get the cat. 2) When you are angry ask her if you can have a few minutes alone to calm down. As hard as it is, you must do this calmly and respectfully. After you have calmed down, talk about the problem with her. She will respect that your are maturing if you act like a young man instead of a yelling, screaming toddler. If the anger persists, ask your Mom to get you professional help before you hurt your Mom, yourself or the cat, etc. Good Luck, being a teen is tough!