Does Islam really say a father can do anything to his child?

Assalamu alaikum, and Eid Mubarak to you all! So I told my dad, "Dad, I love you a lot, but the way you talk to people sometimes isn’t right." He tends to shout and use harsh words with us at home, but outside he’s super nice to everyone. Right after I said that, he started yelling, saying I was being disrespectful because I didn’t like his tone-those were his exact words. When I brought up Islam and having a soft heart, he shut it down, saying, "In Islam, I’m your father and I can do whatever I want to you." He also said we make him angry and sad when we don’t just accept his yelling. It’s been four days and he hasn’t spoken to me. He said salaam today, but no Eid Mubarak. He has other ideas like this too. Once, my mom asked to borrow my lighter for incense (no jokes, please), and he scoffed, "Why did she even ask? She can just take it from you." I said it’s basic respect between people, and he laughed saying, "Are you a person? You’re our child. You’re not a person." I guess my main question is: Islamically, is he right? From what I’ve read in the Quran, it seems like no, but I’d really appreciate other perspectives. Just a note: I love and respect my father deeply. I won’t be sharing more about our family situation because I’m not trying to vent-my only focus is understanding the Islamic ruling on this mindset. JazakAllah khair for any insights.