Why do flight search engines give inconsistent results?

I've been shopping around for flights, and I've noticed that a few flight search engines such as Skyscanner and, in particular, ITA give inconsistent results.
I don't know if this applies to all flights, but in the instance of my trip, ITA shows cheaper results if I choose "plus/minus 1 day" option instead of searching for those three days independently, all else the same. In another leg of my trip, the opposite happened. I was able to find cheaper flights by searching "on this day only" option, and when I chose "plus/minus 2 days" or "plus/minus 1 day", the cheapest options from the "on this day only" option did not show. Why is this and what is causing it? It's making me wonder if I'm actually getting the best possible deal.
I have had similar experiences with Skyscanner, where the price will actually fluctuate a little within a matter of a few hours.
Best Answer
Anecdotally, I've heard that some search engines detect your first search (with cookies or whatever) and give you a very low price and then when you come back to book, the tickets at that price are sold out and they charge you their profit margin more.
They claim it's false, but the sites certainly seem to behave that way at times.
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Airlines. Although travel websites can charge less for the same round-trip ticket because they have access to greater volumes of price listings, they sometimes charge a booking fee that can increase ticket prices.What does +1 mean on Google flights?
If you notice a +1 next to the arrival time listed, on a Google Flights itinerary, it means your flight arrives the next day (or 2 days later if it says +2).Best Cheap Flights Websites NOBODY is Talking About | How to Find Cheap Flights 2022
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