I start from the concept of "freedom". That gets the crux of the concept across quickly.
Note: I have been able to reasonably "explain" the concept, but never been able to "convert" anyone who was not already considering it.
The concept in itself is easy to explain. However it immediately sounds both like a lifetime pain to live like a rabbit AND as scam as well.
They don't believe you can be FI.
So the immediate conclusion is that it's either too good to be true, or ending up having a life full of frustration.
I'd like something simple to kill both these immediate assumptions in a simple and quick fashion. Because as soon as they have these stereotype, they won't dig into long blog post with theory into it.
Step 1: Start from a different topic.
"Do you know how a minimum wage earner can be a millionnaire in 40 years"?
"Well, he could invest $100 per month in SP500 for 40 years. That's how!!"
A lot of disbelief will follow!! You need to break through that first. It is the reality!! So you have an upper hand here as long as the other person cares for data and logic at all.
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Step 1.5: Explain the concept of exponential growth. Don't go mathematical, most people won't understand it. Rather, explain it like "a facet of reality that our stone age brain doesn't understand" - perhaps!!
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Step 2: This has to be at least a month or two (maybe longer, maybe shorter for someone able to grasp the mathematical concept) AFTER the initial shock of exponential growth wears off and the idea that such a thing exists become a part of the existing worldview of the person listening to it.
NOW - the concept of FIRE will sound reasonable, when coupled with the idea that practical and reasonable exponential processes can lead to non-intuitive sums of money over a reasonable time-frame.
Note: It isn't easy!! I had to drag DW kicking and screaming and protesting to this worldview where exponential growth can lead to freedom, and she did have the capacity to understand the mathematical concept!!