Because that's the way the law works. The Florida stand your ground law will let her get off if she can demonstrate that she was fearful. If the woman is aggressively pounding on the door and demanding she come out then it's very easy to use that as a defence and at least one person the jury will likely believe that and she won't be found guilty. As for being able to break down the door, you don't know. Even if she couldn't break down the door, she might have broken a window and forced the door open or gone through a nearby window. It doesn't matter how plausible it is, it's the aggressive behaviour that makes all of that a possibility and what will form her defence.

Other articles provide a bit more context here:

Dispatch: I need you to lock all your doors and windows, OK
Caller: I have
Caller: Her sons said they were going to come and kill me.
Dispatch: And did you know her?
Caller: Yes, she's come after me several times because of her children. Her children keep trespassing over here. They're bothering me and >bothering and won't (expletive" stop")

followed up by:

Caller:"Oh my God, this lady just tried to break down my door. I shot through the door. (inaudible) (heavy breathing, emotions)Yes. The >woman was screaming and yelling, and she was trying to break down my door."
Dispatch: It was a female?
Caller: Yes
Caller: "I didn't know what to do. I grabbed my gun and shot at the door cause I thought she was going to kill me...oh my God.
Caller: I shot at the door because she wouldn't stop. I told her 'get away,' and she wouldn't and (inaudible).

To be clear, I'm not defending her, or saying what she did is right. I'm only saying that with the way the law is, and with the circumstances, it's very likely she'll get off because the victim decided to be aggressive instead of calling the police and letting the police deal with it.