Is it normal that fathers and daughters fight?

I used to butt heads with my dad but he always gets the last word. I fought with my mom and she always outsmarts us and get me the last world. My dad would say hurtful blunt things to me when we fight. When I gave him a heard time he would say, "Back off of me! I'm not putting up with your BS. You're getting too old for that and I will not coddle you! Back off! And walked off of me for something stupid. I got angry for something stupid. I was 18.