Because air travel is the best option in those places.
The shortest commercial route in the world is between Westray and Papa Westray in the Orkney Islands, a distance of 1.7 miles.
If you see the list of short routes , almost all of them are between islands.
That instantly rules out buses and the like unless a bridge is built, which in most cases is not commercially viable.
One can use a boat or ferry, but in most cases, the sea may not be deep enough or calm enough.
aviation.stackexchange.com/users/9731/aeroalias
Most very short distance flights are flown between Islands.
If you have a look at the list of such flight you can see they are places which are not or highly unlikely to be connected by a bridge which may be uneconomical.
Also the flights that are used on these routes are not the average airliners.
They are aircrafts like De Havilland Twin Otter and Cessna Caravan propeller planes which are very efficient at relatively slow speeds and low altitudes.
The ATR42 & ATR72 are examples of large propeller planes in service.
They are meant for short trips with the 72 having a max range of 1500km.
They are also able to land in very short distances.
Ideal for these island destinations
aviation.stackexchange.com/users/None/
Fjords are also a reason these short routes exist, e.g. the trip from KKN to VDS takes less than 10 minutes, vs. driving 165 km (2h 16min according to Google: https://goo.gl/ev5dya )
aviation.stackexchange.com/users/12817/thebjorn
One point not yet mentioned is that most of these short flights are not just between islands, but in archipelagoes.
So an aircraft may be dearer to run than a ferry, but the aircraft can do six or seven journeys a day (e.g. Westray to Papa Westray and back, Westray to Mainland, Mainland to Hoy...) and save the costs of three or four ferries.
aviation.stackexchange.com/users/12807/Tim Lymington
One other rational for unusually short overland flights is that the short hop is a layover to connect two small airports to a larger one.
A few years ago it was possible to fly between Johnstown PA (JST) and Altoona PA (AOO);
which are ~30 miles/60 minutes apart by road.
It wasn't because the airline expected significant amount of traffic between the two towns.
The main route was between Johnstown and Washington-Dulles Airport (IAD) which was flown 3(?)
times a day; one of those flights stopped in Altoona with the primary intent of offering a connection from it to DC.
This stop was cancelled in 2014, and only the direct flight is still offered.
Both airports are very small rural locations and commercial traffic is partially funded with Federal Subsidies , so simple economics aren't the only consideration in the route planning.
aviation.stackexchange.com/users/1396/Dan Is Fiddling By Firelight
I was impressed to read  here  that some passenger airline routes are even below 60 km in length.   Even assuming that the passengers are already in the airport past the security check, probably a good bus could depart from the same gate and arrive to the destination gate in a very comparable time, as the plane still needs to taxi before and after the flight.   Why these short haul flights are reasonable?
What is the rationale behind very short distance flights?
aviation.stackexchange.com
<airline-operations><short-haul>
aviation.stackexchange.com/questions/23970
aviation.stackexchange.com/users/917/h22
Most very short flights are in places where flying is the best option, for example between islands or across fjords. The other rational is a layover to connect between small airporats and a larger one. Very short-distance flights take place when they are the most practical travel option. Most very short-distance flights are between islands or fjords. Another reason for very short-distance flights may be if a stopover is involved.
Very short-distance flights take place when they are the most practical travel option. Most very short-distance flights are between islands or fjords. Another reason for very short-distance flights may be if a stopover is involved.