The Nazis were totally right-wing. Their purges shocked the world. It's not just a left-wing thing, it's a common theme across all forms of extremism. Left, right, religion-based (look at the Taliban now, they don't really fit in the left or right category at all)... It always comes down to the same thing. Not listening to the other person but choosing to silence them with violence instead. The flag they wave is different but the extremism remains the same.
What we need is balance. Left and right together. Agreeing to disagree and finding a way to work together anyway. That's democracy. It's hard but it's the only way.