icanhandthemback
I try not to argue with one of mine because it tends to be her way or the highway. I just bite my tongue although I think I might be getting to the stage where I'll have no tongue left!
My other sibling is not someone I have ever felt the need to argue with. We live very different lives but she's like me, she doesn't like confrontation so we rub along nicely but distantly. Both of us avoid arguments with the other one!
My sister sounds like the first you mention, there is no viewpoint to be considered other than hers. She always has to be right and even if I say we should agree to differ she'll start again. I just don't bother with her now, though I wouldn't refuse to see her or speak to her and we do exchange birthday and Christmas cards.
It's a shame, but she's very set in her ways.