What is the nature of Christ’s sonship?

Concerning the eternal Sonship of Christ, Ryrie has this to say:

I agree with Buswell (A Systematic Theology of the Christian Religion, pp. 105-12) that generation is not an exegetically based doctrine. The concept it tries to convey, however, is not unscriptural, and certainly the doctrine of sonship is scriptural. The phrase “eternal generation” is simply an attempt to describe the Father-Son relationship in the Trinity and, by using the word “eternal,” protect it from any idea of inequality or temporality. But whether or not one chooses to use the idea of eternal generation, the personal and eternal and coequal relation of the Father and Son must be affirmed. Least of all should eternal generation be based on Psalm 2:7 (Charles C. Ryrie, Basic Theology, Victor Books, Wheaton, IL, 1987, electronic media).

Psalm 2:7 reads, “I will surely tell of the decree of the LORD: He said to Me, ‘You are My Son, Today I have begotten You.” The Psalmist’s reference to “My Son” referred to the legitimate Davidic king (2 Sam. 7:14) who one day would reign in the person of Messiah, who, of course, is the Lord Jesus. The words “Today I have begotten You” speak of the day of coronation or the anointing of the King to be fulfilled in the Millennium. But in the New Testament, this is related to Christ’s resurrection (Acts 13:33-34; Rom. 1:4; Heb. 1:5; 5:5). Many theologians or Bible students see Acts 13:33 to refer to Christ’s exaltation via the resurrection because it clearly validated Jesus’ claims and marked Him out as the Son of God as Paul demonstrates in Romans 1:4.

Becoming flesh made Jesus Mary’s son, but not God’s. This would suggest He had not been the Son of God and true deity prior to birth. Christ’s title as Son of God is a strong affirmation of the deity of Christ. Also from Ryrie’s Theology is the following:

Son of God. Our Lord used this designation of Himself (though rarely, John 10:36), and He acknowledged its truthfulness when it was used by others of Him (Matt. 26:63-64). What does it mean? Though the phrase “son of” can mean “offspring of,” it also carries the meaning “of the order of.” Thus in the Old Testament “sons of the prophets” meant of the order of prophets (1 Kings 20:35), and “sons of the singers” meant of the order of the singers (Neh. 12:28). The designation “Son of God” when used of our Lord means of the order of God and is a strong and clear claim to full Deity. “In Jewish usage the term Son of . . . did not generally imply any subordination, but rather equality and identity of nature. Thus Bar Kokba, who led the Jewish revolt 135-132 B.C. in the reign of Hadrian, was called by a name which means ‘Son of the Star.’ It was supposed that he took this name to identify himself as the very Star predicted in Numbers 24:17. The name ‘Son of Encouragement’ (Acts 4:36) doubtless means, ‘The Encourager.’ ‘Sons of Thunder’ (Mark 3:17) probably means ‘Thunderous Men.’ ‘Son of man,’ especially as applied to Christ in Daniel 7:13 and constantly in the New Testament, essentially means ‘The Representative Man.’ Thus for Christ to say, ‘I am the Son of God’ (John 10:36) was understood by His contemporaries as identifying Himself as God, equal with the Father, in an unqualified sense” (J. Oliver Buswell, A Systematic Theology of the Christian Religion [Grand Rapids: Zondervan, 1962], 1:105).

There are many other ways and passages to support the deity of Christ, but the point here is that this title clearly does that. It does not and cannot, as it is used in the Bible, refer to Him as a son by the incarnation. The incarnation did not make Him Son of God, it was the means that the Son of God became man that He might die for our sin.