I am quite surprised that no-one mentioned safety as a reason in the previous answer. In 1996, the FAA adopted Amendment 25–87, which imposed additional high-altitude cabin-pressure specifications, for new designs of aircraft types.
The standards adopted as Amendment 25-87 pertain to operation of subsonic airplanes to a maximum altitude of 51,000 feet, although many of the requirements addressed therein relate to operations at lower altitudes (below 41,000 feet) as well.
Typical systems to be considered are engine bleed air systems, air conditioning systems, power sources, outflow valves and their associated control systems, etc. Failures or a combination of failures which expose the occupants to: (1) cabin altitudes in excess of either 25,000 feet for more than 2 minutes, or (2) cabin altitudes that exceed 40,000 feet for any duration, shall be shown to be extremely improbable (see Glossary).
Airliners altitude are thus limited by safety regulations in case of rapid pressure loss. On modern airliner a major engine failure might lead to a quick depressurization and even passenger sucked out of the window. In this case you have to lower the altitude below 25'000ft in less than 2 minutes which means a decent rate of approximately 10'000ft/min. To avoid any structural overstress, you can't have much higher decent rate than that thus limiting the maximal altitude you can fly. The 40'000ft absolute limit is not unbreakable as the A380 was certified to fly at 43'000ft.
On the other end private jet have the engines mounted on the aft fuselage, and behind the pressurization bulkhead. Which means that fast depressurization in case of an engine failure is totally unlikely and they can therefore bypass this rule. Furthermore they operate at higher cabin pressure which means in case of an air pressurization system failure, they will have a bit more time to descend to lower altitudes. Therefore they can use higher altitude up to 51'000ft to avoid traffic and increase fuel efficiency.