The Story
In addition to nitrogen, the air we normally inflate our tires with contains oxygen and small amounts of water vapour and other gasses.
Water vapour can condense into liquid water, causing wheel rims to rust. As temperatures change, the conversion from ice to water to vapour and back again can affect tire pressure.
Oxygen can attack the rubber from the inside of the tire, making it weaker and more likely to burst.
In addition, should any hydrogen sneak
into the tire, it could combine with the oxygen to make water.
The nitrogen molecule is larger than other gasses, so it will be retained in situations where microscopic leaks allow oxygen and other gasses to leak.
Generally, nitrogen filled tires provide improved fuel efficiency, less tire wear, better handling and performance, extended tire lifespan, and extra safety.
Facts
Amazingly, all of the above facts are true.
Where they fail is in the degree to which they are true. In practice, the difference between filling your tires with normal air (about 80% nitrogen) and with nitrogen (about 95% nitrogen) is insignificant.
Yes, airlines are required to use nitrogen in their tires, but that's because of two factors that car drivers will never encounter. Large aircraft tires can get very hot during landing, and if one should burst, any oxygen within the tire could contribute to a fire, which in that situation could be catastrophic. At high altitude, aircraft can become very cold (e.g. 60 degrees below zero), and any water vapour in the tires will freeze, slightly lowering the air pressure in the tires which could have an effect during the critical few seconds when aircraft tires are actually used. Aircraft tires are built to work almost perfectly for brief periods of extreme conditions. Normal automobiles never encounter situations anywhere near that.
When was the last time you heard of anyone ever having their wheel rims rust away because of moisture in the tires?
If oxygen can attack the rubber inside a tire, what about the oxygen that is constantly surrounding the outside of the tire? Surely that is a much more severe problem, yet the only way it could be a real problem in practice is if your car is rarely driven and has tires that are many decades old.
And even if any of these effects were of significance, note that for the most part they are self-correcting. If oxygen attacks the interior rubber or causes rims to rust, that means that soon the oxygen will all be used up by these processes and no longer be a concern. Similarly, if other gasses leak faster than nitrogen, that means that an air-filled tire would soon be filled with almost pure nitrogen anyway.
Why
Tire centers provide air (which is 80% nitrogen) for free, or at a very low cost. But if you believe that 95% nitrogen is a much better product, they can charge large amounts of money for it.