Intellect that is devoid of emotional conviction leads to cynicism and hedonism. Amalek's two great proteges. We have a genuine claim to the Land of Israel. And yet all our valid arguments sound like rhetoric and propaganda. And every day Jewish blood is spilled.
Jewish blood is still cheap.
However, they are called 'barren' because after all was said and done, it was as a result of their prayers that they eventually conceived and gave birth to children. At that point it was evident that they weren't barren at all, rather that Hashem had wanted their prayers and had therefore withheld children from them. However, if they had not merited children even after they had prayed , one couldn't say that their 'infertility' was because Hashem desired their prayers. For it could well be that her infertility is only a sign that Hashem desires her prayers. She herself has cause to sing, because her infertility is a sign that she is a very elevated and righteous soul.