I find it hard to be friends with her

I have a friend, 'L'.

She is generally self assured, confident, and loud/extroverted.

But sometimes I feel she can be stubborn, and that she can be quick to yell.

Whenever I debate with her, she ends up yelling her point louder and louder. She doesn't make an effort to listen to my side of the argument.

When she is talking, I try to understand her ideas. When I try to suggest something different that she doesn't agree with, she immediately shoots me down and tells me why my ideas are wrong.

I understand I am not always right, I try to listen to her, but I feel as if she is not open to my criticism.

I feel she is not open to hearing my full arguement, when she decides that I am wrong, she will make a huge deal about why I am wrong.

I am okay with constructive criticism, but I feel there isn't much constructive to her criticism. It feels at times she is flat out yelling at me, scolding me, or even talking down to me and trying to make me feel stupid/humiliated.

When she starts talking down to me I try my best to have a level head. I try to calmly dxplain to her my ideas. She has none of it.

She has a habit of (rudely) interrupting me, she doesn't even let me finish my sentence. I find most of the time I need to cut her off and talk over her for my point to get across. 

Even when she is 100% in the wrong, she won't back down easily in my opinion. She can be a little stubborn.

What can I do? I feel unheard and unappreciated when I try to debate with her. She doesn't like listening to me after she decided that I am wrong.

I want to be more assertive with her. But I need advice. What are your thoughts?