They are not necessarily lying, but they are clearly an outlier. My spending is maybe a few percent higher and prices for some of the things I buy are even down recently. Everyone has a different experience, which is why we have aggregate statistics to quantify what the overall effect is.
I generally agree that CPI "feels" to be consistently lower compared to what actual people experience.
But you can't have a meaningful discussion about it if you do not list the weight of the price hike in your expense pattern.
When gas for your car normally takes up 10% of your income, and this price doubles, your personal inflation is 10%, not 100% (assuming no other price hikes).
Just to be clear. The person did not say it his personal inflation is 100%. He said prices increased by 100-150%. If item X usually costs $3 and now it costs $6. The price of that item increased by 100%.
Perhaps he is only spending 10% of his income, but it doesn't really matter for what he is talking about.
What he implied with the term "conspiracy theory" in relation to inflation is that there's a vast mismatch between reported CPI and experienced CPI, hence the reported CPI is a conspiracy theory or corrupted.
Typically statements like "this increased 100-150%" are used to support the theory. The only thing I'm saying is that individual price hikes are meaningless without any information about the total expense breakdown.
That said, I do agree that CPI is typically slightly optimistic.
Gas prices doubled in my area (Southern California) for a short period of time a few months ago. Some of our gas stations were just a few cents short of $7. They have now down a bit (in the $5 - $6 range), but at one point it did get to double. I don't have any receipts to give you the exact dates and prices though.
I would say that you can't just look at average prices for the US. Look at the California version of that chart [1].
July 2021 to July 2022 is an increase of about 38%.
If you look at June to June it is 50%.
While not double, it is quite a bit more than 30%. Depending on the area the person quite possibly did recently experience double the price like I did.