She's not spouting this because it's rational.
If there's anything I learned from my experiences in organized religion, the skeptics' society, various mental institutions and a career in criminal justice, it's that confronting irrational targets (or salesmen!) just teaches them how to better-reinforce their own flawed arguments and behaviors. They learn what rational people will come at them with and learn how to counter or subvert it, which helps them become even more persuasive to their next mark. Now they sound more intelligent and authoritative, which is precisely what makes them so dangerous!
The same advice applies to internet trolls. It's hard because it's instinctual, but never engage-- smile and walk away. Don't give them an opportunity to learn how to exploit or undermine the thought patterns of a rational person. If you don't yourself drown in their sea of circular logic, you're just giving a malicious organic learning algorithm free training data at the expense of your time and sanity.
If you starve them of attention, they can only feed off of each other-- to predictably amusing ends. Without outside input, then like any cult, they eventually become an incestuous feedback loop of lunacy that deviates so far from societal expectations of normality that you no longer have to convince anybody of anything since they do it for you.
It's true that I generally don't engage with people who believe in a flat earth or who claim to be absolutely certain that the government is colluding with extraterrestrials, simply because I doubt any good would come of such an interaction.
IMO that excludes all flat Earthers, at least those who have received a primary school education.
Dehumanizing or disrespecting others is one of the easiest dangers, as is challenging with a incomplete or fallacious counter.
These only add fuel to the fire.