In addition to other answers...
There are also fewer airplanes today, so fewer seats.
And airlines are a very "supply and demand" business, so normal demand with fewer seats to sell will cause prices to go up.
Why fewer airplanes? In March 2020 when the world stopped, it was crunch time for airlines. Normally when you store an airplane, you fly it to a place where environmental conditions favor preservation - Mojave Airport, Pinal Airpark, Kingman, Tureul, APAS, etc. Of course these locations instantly filled up and airlines all over the world were forced to park airplanes "any which where they can" (that can take a widebody), and you famously saw popular airports with whole runways closed and used for airplane parking. This had 2 problems.
- Parking fees at such airports are quite high.
- Maintenance increased, because weather at these airports was less favorable to storage than the preferred Mojave, APAS etc.
Keep in mind you don't just park an airplane and forget it for a year, unless you want to do a very costly and laborious systems check when it returns to service. So the planes need to be regularly maintained, serviced and exercised. It's really best to keep a plug-in HVAC pack on it (I bet some airports were scrambling to get more electricity out to ramps for that)... and run up the engines from time to time. Being parked does not pause the countless periodic maintenance items.
So airlines accelerated retirement of older planes
These parking and maintenance costs are terrifying to airlines trying to figure out how to avoid bankruptcy.
As such, airlines were in a big rush to sell the "tail end" of their fleet - planes that were going to come out of service in the next 2-10 years anyway due to normal replacement cycles. They already had orders into Boeing and Airbus for those planes' replacements.
Selling the plane means somebody else pays storage and somebody else pays maintenance (or not, and made it a "parts picker").
The "pickers" are being flown to those "fair weather" boneyard airports like Mojave and Pimal who tolerate "Pick Your Part" operations on their ramp... (unlike DeGaulle or Detroit Metro who definitely don't). That in turn forced "runners" to poorer-weather airports and increased their maintenance and parking costs.
However, new plane construction can't be accelerated much
It would be grand if Boeing and Airbus could just "turn production to 11" or "throw three shifts on" and rapidly replace those early-retired jetliners now that we need them. But the business doesn't work that way. Lead times are quite long and inertia is very high.
Also, we're in the middle of a supply chain nightmare generally, two very large Eastern European technology producers are in the middle of a war, and oh - speaking of that, the Antonov-225 super-transporter, which sometimes pinch-hit to move airplane parts, was wrecked.
So supply, which will take years to recover, is simply far out of sync with demand, which has been wildly whip-sawing all over the place as we alternate from "done with COVID, let's get out again" and "Oh wait, COVID came back for some reason". As someone with a side business in tourism, I can say we've actually been doing this all along. Just now, it seems new. It seemed new everytime.