To Timothy, my beloved child: Grace, mercy, and peace from God the Father and Christ Jesus our Lord.
Paul asserts his apostolic authority not for Timothy's sake alone; Timothy already believed. He writes with these grand titles because he stands at death's door and means to seal his whole ministry with his blood, that the Church may know his doctrine comes from God Himself, not from a mortal man's opinion.
AI summary
Commenting on 2 Timothy 1:1-18
Here is, I. The inscription of the epistle Paul calls himself an apostle by the will of God, merely by the good pleasure of God, and by his grace, which he professes himself unworthy of. According to the promise of life which is in Christ Jesus, or according to the gospel.
Commenting on 2 Timothy 1:1-5
To Timothy, my dearly beloved son,.... Not in a natural, but in a spiritual sense; and not on account of his being an instrument of his conversion, but by reason of that instruction in the doctrines of the Gospel which he gave him, it being usual to call disciples children; and he calls him so, because as a son, he, being young in years, served...