Why aren't I allowed to get angry at children?

I am a 17 year old woman. I was babysitting an 8 year old girl and she said to me "Barack Obama is president of the United States." I told her that she is correct, and she said "That makes me sound really smart right?" I didn't want to lie to her, since most kids around here know that by age 8, so I just said "It makes it sound like you know your politics." She said "That makes me sound smart, right?" I told her to define smart, and she said "Like, good at math." I told her I couldn't answer that question, since she didn't tell me her math skills, although I doubt she's bad at math, and then she got extremely angry. She lunged at me, punched me (I got a black eye), saying "YOU KNOW WHAT I MEAN!!" I told her I didn't know what she meant and what she was doing was immature and completely unacceptable. I told her she had to go to bed at that point. However, as I started walking up the stairs with her, she kicked me down and I got my foot caught in between the poles going up the railing, causing me to twist my ankle. I was unable to make it the rest of the way up the stairs, so I called the mother and explained to her what happened. She just told me "I can't believe you aren't taking responsibility for this. You are the adult here, not my 8 year old daughter. Get upstairs!!" I attempted to drag myself up, but I don't have enough upper body strength. I had to wait for the mother to get home a couple hours later. When she got home, she went upstairs and the entire bathroom had been destroyed by the child. She started yelling at me, repeating that I am the adult and I shouldn't have been so immature and just gone up the stairs. She kicked me out, refusing to pay me. Of course, I couldn't walk home, so I called my parents to come pick me up. When I explained what happened, they said the same thing, "You are the adult, you should be taking responsibility. Don't get angry at the kids and don't blame them for what happens!" What did I do wrong, and why aren't I allowed to get angry at children?