Is this considered self-defense? Can a school give this suspension?

My friend was walking down the hall before homeroom and a girl who she has issues with started calling her, "b*tch" and saying "come here". My friend ignored her and continued to walk down the hall. The girl started to push her and my friend told her to stop, which she didnt right away. They then started to argue with each other and eventually the girl hit my friend, threw her to the ground, and was on top of her "punching her". My friend was fine and was eventually able to return to cles. Towards the end of school, no one saw my friend anymore and we found out she also got expelled. The principals said that on the video it shows that my friend hit back after the girl first hit her, and that self defense is "pushing" not "hitting", so she got suspended for 3 days. Is this unfair? If someone hits you, your reaction is to hit back, and my friend tried to avoid the situation in the beginning If someone is going to hit you, pushing them away isn't going to help you.Any thoughts?