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This Divine ownership of our children obviously has sacramental implications, but leaving that aside the passage I referenced above has to do with an unfaithful Israel failing to bring their children up in the Lord. At the time of Ezekiel's prophetic ministry judgement was falling on Judah for their unfaithfulness to God. Particularly, in chapter 16 God highlights their pagan parenting as one of the charges against the people meriting judgement. Judah and Israel were taking children who belonged to God by virtue of the covenant and raising them to be idolators, even to the point possibly of sacrificing them to pagan gods.
We can learn from this that raising our children up in the context of faithfulness is one of the greatest blessings we can bestow upon them as well as the form of obedience all Christian parents are called, this is because the children we have are essentially talents God has given us on loan to be good stewards of. This means their education must be distinctively Christian as well as their speech, manners, dress, play and entertainment, Christianity is for the whole man and all of life.
How different parents apply attempting to faithfully raise their children in these areas will differ, but the point should be clear that we all should be seeking to apply the gospel every area of our children's lives. That is after all what is means to say "As for me and my house, we will serve the Lord". That is not just a verse worthy of an aesthetically pleasing doormat or wall hanging, rather it is a call to multi-generational covenant faithfulness, brothers and sisters may we labor for such a legacy lest Ezekiel's outcryings against unfaithful Judah equally fall upon us.