God promised as far back as Genesis 12 to bless all the families of the earth through Abraham and his descendants. The promises that God gave to Abraham went with a serious responsibility to ‘command his children and his household after him to keep the way of the LORD by doing righteousness and justice’ (Gen. 18:19).
Raising up children for Abraham and teaching them to walk in his ways was a serious business, and the whole Old Testament, from Genesis to Malachi (e.g. Mal. 2:15), is full of reminders of how important God saw it as being.
Which is why John the Baptist’s words in Matthew 3:9 are so jolting. God doesn’t need Israel and the children of the Israelites. If he wants to, he can raise up children for Abraham from the stones by the side of the Jordan river.
At one level (a bit like the story of the virgin birth) John’s words function as a huge challenge to human fatherhood and family. Viewed as an end in itself, human fatherhood and family is an idol that God is perfectly prepared to cut down and bypass.
At another level, John’s words are an urgent call to take the business of raising up children for Abraham a whole lot more seriously. The fact that God has an axe at the root of the trees, ready to cut down the trees that don’t bear fruit, is not a reason to give up on being a tree. It’s a reason to bear fruit.
No-one is automatically a child of God, simply by virtue of being born into the right family - this side of the cross, as the gospel goes out to the nations, that is even clearer than it was in John’s preaching. People enter God’s family not by birth but by the new birth, through the work of the Spirit (cf. John 1:13; 3:6; Rom. 2:29). But the normal means by which the Spirit works is through God’s word (cf. 1 Peter 1:23), which can be learned from infancy and is able to make a person wise for salvation and equipped for every good work (2 Tim. 3:15-16).
So whatever else we fathers do in our lives (including our ‘ministry’ lives), we ought to be praying for God’s Spirit to be at work in our kids’ hearts to give them saving faith in Jesus, and teaching them (by word and example, with discipline and patience) what the word of God says and how to believe and obey it.
If we do everything else except those things, then our fatherhood is falling catastrophically short of what it was created for. John’s words to Israel carry an echo that functions as a warning for us. God offers no guarantee of permanence to half-hearted faith and obedience half-heartedly passed on from generation to generation. There is an axe at the root of the tree.
