@layman,
Their own theory SAYS the moving clock runs slower. Logically AT LEAST ONE of the two twins MUST be moving.
Therefore, relativists contradict their own theory when they say "both are correct." There's a reason for that. I have also quoted Physics Professor Morin (from Harvard) who explains the "reason."
It is this. Without those two conflicting and contradictory claims, the whole SR theory falls apart. It is only by making such claims that Al can claim that the speed of light is constant in all frames. You must have two subjective observers, each presupposing a different set of "facts," to make that (constant speed of light) appear to happen.
So, relativists try to have it both ways. On the one hand, they want to say that "both are correct" and "there is no way to tell who's (relatively) moving." On the other hand, they want a theory that doesn't contradict itself and that can make predictions which have some meaning (which you can't do if you don't even know who's moving).
In trying to maintain both positions, utter sophistry results. The so-called "explanations" of the twin paradox show this clearly. After all the inadequate "physical" explanations fail, they are left with trying to point to a piece of graph paper to "explain" the inexplicable. Al himself rejected that attempt.