Have I raised a bully?

I've always heard that girls are meaner than boys, and I thought people were just being silly when they said that. But now I know it's the truth. As you read the post, keep in mind she's only 2 years old.

My sweet, little Avery....or my not-so-sweet little bully Avery...is causing some heartache for me right now. When I picked her up from daycare yesterday, her teacher told me she had not had a good day. She was hitting other kids and making grunting noises (didn't know I raised a pig) and if a kid would hit her, she would just have a complete meltdown. WHAT? A girl having a dramatic meltdown when things don't go her way? I can't imagine....
But anyway, I picked her up and it looked like she was getting sick, or at least that's what her eyes were telling me. They looked weak, watery, and her right one was matted a little bit. But off we go to the pizza party, and she is A-OK! Running from one end of the room to the other and having a jolly ol' time. When we get home, I tell her daddy what all happened at school, and the only thing he heard in that conversation was that someone hit his baby girl. So he proceeds to sit her down and tell her that if a child hits her, it's ok for her to hit back (we do teach our children to NEVER instigate a fight, but you must always defend yourself). And like father, like daughter, all she heard was that it was OK to hit.
So off we go to daycare today, and I call to check on her. I can tell in the teacher's voice that what I'm about to hear is not gonna be good. "Well, we've had a few instances already today and she's instigated all of them". Oh dear.... a flash forward of Avery Dunn, serial killer, pops into my head. I shake it off. "She has been hitting all the other children for no reason and when they try to defend themselves by hitting back, she gets mad. She doesn't understand that they are trying to protect themselves". Silence.....I have NO idea what to say to the teacher, but "Ok, I have raised a bully. I gotta go now so I can call her daddy about this".
I call Kevin to tell him all of this, and at the same time I tell him about some good news I just got at work. Well, never mind that his daughter is turning into Avery Ali, let's talk about your work news! HELLO Kevin! Your daughter is causing fights! What is it with daddy's and their little girls? Can they seriously just get away with whatever and it be ok?