I feel shunned by my friend so I'm going to cut her out of my life.
Why don't you want to be friends with her?
She never answers my phone calls.
It would be a shame to end the friendship without seeing if it can be fixed. Be open with your friend about how you are feeling, maybe she will change the way she's treating you.
I don't want to be a pushover; I'm asserting my dominance.
I think you could benefit from speaking to her about the issues she is causing as that's a great way to show you are not a pushover. Then, if the situation doesn't get better, ending the friendship would be reasonable.