Jesus IS a Father. He is the Father of creation.
Luke 3:38 (NIV)
38 the son of Enosh, the son of Seth, the son of Adam, the son of God.
Adam the son of God the Word. Not son of God the Father.
John 1:14 (NASB95)
14 And the Word became flesh, and dwelt among us, and we saw His glory, glory as of the only begotten from the Father, full of grace and truth.
God the Word Father of creation became a Son in the incarnation.
God the Father was not a Father until God the Word became the Son in the incarnation. Before that, God the Father was (for lack of another description) God the Authority.
The Holy Spirit is also a Father. He is the Father of revelation.
2 Peter 1:20-21 (NASB95)
20 But know this first of all, that no prophecy of Scripture is a matter of one’s own interpretation,
21 for no prophecy was ever made by an act of human will, but men moved by the Holy Spirit spoke from God.
He is the Father of the Bible. God the Author.
From the very beginning was:
God the Authority.
God the Word.
God the Author.
We look back through what they became since then and apply the names as in 1 John 1:2 "the Father" etc.
This also answers the age old challenge how Jesus could be called Everlasting Father....
Isaiah 9:6 (NASB95)
6 For a child will be born to us, a son will be given to us; And the government will rest on His shoulders; And His name will be called Wonderful Counselor, Mighty God, Eternal Father, Prince of Peace.
He is the Father of Creation, but he is not God the father (who is Jesus' actual Father of his physicality). We are children of God the Father through adoption. But Jesus (the man) by direct creation. This is how and why he made the distinction between relationship to God the Father:
John 20:17 (NASB95)
17 Jesus said to her, “Stop clinging to Me, for I have not yet ascended to the Father; but go to My brethren and say to them, ‘I ascend to My Father and your Father, and My God and your God.’ ”
To my Father
and your (adopted Father)
To my God
and your (adopted God).
Romans 8:23 (NASB95)
23 And not only this, but also we ourselves, having the first fruits of the Spirit, even we ourselves groan within ourselves, waiting eagerly for our adoption as sons, the redemption of our body.
Romans 9:4 (NASB95)
4 who are Israelites, to whom belongs the adoption as sons, and the glory and the covenants and the giving of the Law and the temple service and the promises,
Ephesians 1:5 (NASB95)
5 He predestined us to adoption as sons through Jesus Christ to Himself, according to the kind intention of His will,