Most of SR demonstrates a symmetry. The contractions and
dilations one oberver supposedly sees for another system,
are exactly what the other system sees for him.

The Twins Paradox says, however, that this symmetry fails.
If the travelling twin left at t=0 and returned at t=100,
then t'=g(t-xv/cc) and t' > t, which would say that the
travelling twin's clock is ticking away faster. The symmetry
would say the traveller sees the stationary clock ticking
away faster than his.

However, the traveller has to change direction, and thus
by magic, as it were, the supposed lack of simultaneity
forces the travelling twins clock to somehow be the ruling
clock.

As we have seen on a number of grounds, the idea that
simultaneity does not hold across inertial frames is
absurd, and the correct use of generalized coordinates,
which preserves ratio scale quality shows it to be
true that simultaneity holds reign.

There is no lack of simultaneity, and there is no
differential aging of such twins.