I think there are two reasons why we can say that Christians are the “true children of Abraham”. First would the the traditional way of interpreting this thought and that would be connected to our faith. Since Abraham was declared righteous because of faith, those people who demonstrate that same faith would be his true descendants rather than those who are physically descended from Abraham but do not have faith.
The second reason is because Jesus is the promised seed of Abraham and as Christians we are in Christ, and thus we are part of God’s promised descendants to Abraham. Ben Witherington wrote:
“Paul returns to the them that they have in Christ the heritage of Abraham, indeed they are in Chr-ist the ‘seed’ of Abraham. Christ had previously been called the seed of Abraham (3.16) but since Paul views Christ as an incorporative personality, and since they are in Christ, they are also that seed promised to Abraham, having become in Christ the legal heirs of Abraham and the promises given to him. This verse reminds us, especially when coupled with vs. 26, that Paul is once more transferring the language applied formerly only to Jews to Gentiles, and claiming they already have the benefits that accrue from being brought into the family of Abraham” (p. 281; Grace in Galatia)
So we are Abraham’s true children because of our faith in Christ Jesus, the promised descendant of Abra-ham, who will bless the entire world.