Two twins of the same age start on planet Earth. Twin A stays on Earth while twin B travels far, far away and back at near the speed of light.
Because of Special Relativity, A looks at B's clock, and it moves slower than his own. So at the end of B's journey, A is much older than B.
However, B's frame of reference is equally valid. According to B, A's clock is moving slower than his own. So at the end of the journey, B is older than A.
What faulty reasoning leads to this apparent contradiction?