Well, to be honest, I don't think most of them really knew why. It was what their teacher said to do, it worked for him, they did it and their aikido worked for them. .
And as for the scientific reasoning behind the effectiveness, perhaps this will be more helpful:
"If you tense up the arm, you are tightening both sets of muscles, the triceps and the biceps. The triceps are trying to keep the arm straight, the biceps are trying to bend it. When someone attempts to bend your arm they have a secret, unwitting ally in your biceps. Of course they can bend it, your biceps are inadvertently helping. When you stop tensing and use the Ki metaphor, you only use the triceps, and you're not fighting yourself. You become stronger, much stronger. "