I am reminded of your sincere faith, a faith that dwelt first in your grandmother Lois and your mother Eunice and now, I am sure, dwells in you as well.
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
When I call to remembrance the unfeigned faith that is in thee,.... This caused him to give thanks to God for it, whose gift it is and made him the more desirous of seeing one, who was a true believer, and an Israelite indeed.