well first of all I dont know whether everyboy here is really convinced :

The twin paradox is not a paradox but the plain truth
The pilot returning on the earth is really younger than his twin brother

Are you asking why is it ?

Nobody can really grasp this claim being something beyond our experience

It is not possible to provide an intuitive explanation just a logical explanation is possible , namely :

The symmetry of the observers

At a first glance all of us assume that an observer on the earth is somehow different than an observer on a train

However if you figure out two starships in the deep space there is no way to distinguish them
You can just claim that they are in a relative motion

If the two starships observes the same event, for example a super nova then they can meeasure a differnt duration of the event
However their measures must be symmetrical otherwise you could distinguish the two observers

There is one only way to make the symmetry of the observers compatible with the speed of light, being a costant :

The time on board of the two starships must flow in a different but symmetrical way
The identity is of course a special case off symmetry

In other words

The first pilot claims : the time on board of the other ship flow slower than my time
The second pilot claims : the time on board of the other ship flow slower than my time

It is not something that we can understand it is something that we must accept