AITA for telling my dad that he was wrong for calling my cousin stupid

So context. My cousin (10 F) just got a baby shitzu that she immediately loves dearly and she's actively learning how to take care of the puppy and I think she's responsible enough to take care of something like a puppy.

Me (17 F) and my cousin are close and love pets and we can't stand seeing pets get pushed around or hit but our whole family is quite different..

For example my grandmother had hit my cat for just laying on the table.. I typically spray my cat with water since I don't want to hit her but my grandmother had hit her to get her off.. I told her not to do that because I dont think hurting the cat just to get it off the table was needed.

Eventually my grandmother told on me to my dad and aunt who got angry at me, my grandmother lied that she didn't hit the cat but lightly pushed it..

Now I'm gonna move to the actual story.. my cousin had learned that shitzus need to be in a cold room, but in our country it's typically very hot, my cousin had told me that she wanted to put the dog in our room ( me , my father and her share a room with an AC )

Her shitzu is in a big cage rn now but has a bed, water bowl and food.

I told her why not ask her parents since it was their room and it was her dog, she had told me that our aunt and grandmother wouldn't let her.. my mistake was telling her to go up to them and tell them that it was her dog and that her parents had agree (which they did)

She came back frowning and said that our grandmother had told her to stop forcing things and my father (45 M) had joked to put it beside her on the bed..

My dad came in to take a shower in the attached bathroom and had asked my cousin why she wanted the dog in the room, my cousin explained that she didn't want her puppy to die since she learned that she wanted the dog to be comfortable.

My dad then called her tanga translation ( she called her stupid)

I defend my cousins telling him that she was a child and he didn't need to call her stupid, but my dad defended himself that it was a expression. I agrued that it wasn't an Expression an expression would be something like "I'm so stupid" not "you're stupid" because that was an insult.

I told him that I thought he went to college and he said he did but he kept arguing that he was in the right and that I was wrong I gave up and just shut my mouth because I couldn't handle his arguments.

I just went to comfort my cousin and told her that her shitzu wouldn't die randomly and told her. To wait for her parents delivery for the pampers and call cage for her dog so it would sleep in the room

Anyways.. that was all what are your thoughts..?