In my experience, it's easier to start by questioning what "authoritarian" even means. All societies and political structures rely on authority to maintain social control to greater or lesser extents. A really good example of this is asking what is the difference between a tax collector and a armed robber. Both demand money from you and threaten violence if you don't give it to them. The main (and some would say only) difference is in authority. The tax collector has authority, the robber does not.

Then, question where liberal "democracy" derives its authority from. Most libs will claim that it comes from the approval of the people or the democratic mandate (same thing, really). That's when you can question why studies repeatedly show that there is no correlation between popular opinion and policy. Show them polls of how most Americans want public health care and ask why it never passes.

Lastly, you can raise the question of whether liberal democracy actually has any democratic mandate if it does not in fact follow the will of the people. If there's no democratic mandate, then what actually separates a liberal democracy froma dictatorship where one party keeps getting voted in because they fudge the votes? The people can vote a guy out? And what? Replace him with a different dude who won't do what the people want?