Matthew Poole and continuators on Luke 1:7

7 And they had no child, because that Elizabeth was barren, and they both were now well stricken in years.

Amongst all Earthly Blessings, there is nothing we more desire then Children, in whom we have a kind of Perpetuity, living in our Species and in our Posterity, when we are dead in Nature; but as God for our Tryal, doth often deny us other good things which are the great objects of our desires, so he doth often deny his own People this great Blessing. Sometimes he withholdeth it a long time from those to whom he at length giveth it. Barrenness in Israel was a Reproach. See v. 25. and 1 Sam. 1.6. There was a promise to Abraham of a plentiful Seed, hence amongst the Jews, she that was Barren hardly thought her self, or was judged by others a Genuine Daughter of Abraham. Both Zachariah and Elizabeth, were now well stricken in Years God chuseth this Woman naturally Barren, and now Aged, also, to be the Mother of Iohn the Baptist, therein working a double Miracle; and it is observable in Holy Writ, that when God denyed to any Women Children for some long time, and then opened their Wombs, they were the Mothers of some Eminent Persons, whom God made great use of. Thus it was with Sarah, Rachel, the Wife of Manoah, Hannah, 1 Sam. 1. and this Elizabeth.