User blog comment:Kaido King of the Beasts/Chapter 802: The Elephant in the Room/@comment-67.204.208.3-20151002134122

Another thought:

Whitebeard wanted a family more than anything; he treasured his crew as his sons and daughters. So it seems really strange to me that he would not have children of his own, and even stranger that he would abandon them if he had.

Based on that, the only thing that makes sense to me is that Whitebeard was sterile.