I am not going to do all of the verses, but here are the points that I saw that Paul makes in 2nd Timothy chapter one.
- He really wants to see Timothy again. Verse four.
- Timothy has a strong faith (unfeigned faith), and his grand-mother and mother also believed. Verse five.
- Paul writes about the spirit that God gives us (not a spirit of fear, but of power, love, and a sound mind). Verse seven.
- He tells Timothy not to be ashamed (of the testimony of the Lord, and of him). Verse eight.
- He says that he is not ashamed (of his sufferings). Verse twelve.
- He tells what he is (Preacher, apostle, and teacher). Verse eleven.
- He tells Timothy to "hold fast to sound words...in faith and love..."(to tell others about God, just as Paul has told him). Verse thirteen.
- He writes about the many people who deserted him (including Phygellus and Hermongenes), and the one who was faithful (Onesiphorus). Verses fifteen through eighteen.