Not agreeing or disagreeing, because I don't really want in this discussion, I was just passing by and saw what could be a miscommunication. What I think they were trying to say is the logical inversion of what they actually said, which would be: [Fascism has an extremely hard time rising under authoritarianism]
What they said, "fascism emerges from liberalism" reads as "fascism ALWAYS emerges from liberalism" which I feel like is... Really loose speaking, I think. I could be wrong.
Maybe any non-authoritarian control does ALWAYS result in fascism. You would have to do the statistics on all history and human behavior. It's definitely possible to be true. I think there may be, I recall something about plato or socrares or ancient Greece or something talking about how a tyrant will ALWAYS rear its head or something.