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The classic stereotype is that the mother is loving and caring, but the father is a stern disciplinarian. A father’s encouragement, however, can be one of the greatest motivations in a child’s life, just as is a mother’s love and compassion. Paul uses three participles to describe how he was like a father to the Thessalonian church.

Exhortation is something like a cheerleader, someone that builds another up and says “you can do it!” Think of the father who is trying to encourage his child to have confidence playing baseball for the first time – he builds the kid up and pushes just a bit so that there is confidence to “step up to the plate.” Paul had to do that with his congregation: He prodded them and pushed them to live a life honoring to God, especially since some aspects of the Christian life are strange to the Greco-Roman world.
Second, Paul comforted the church. By comfort, Paul is looking more at cheering someone up, consoling, or helping someone who is experiencing a difficult time. The verb is used in the context of comforting someone who has suffered a loss, a death or other tragic event. For example, in John 11:19 people came to comfort Mary and Martha after the death of Lazarus.

Third, Paul charged you to live lives worthy of God. Paul’s “urge” is “to be emphatic in stating an opinion or desire; to insist on” (L&N). When your father expressed his opinion on a topic, he often was not offering something for discussion, he was telling you what you ought to be doing, perhaps phrased in the form of an opinion. That is what Paul did as well. He showed from the Scripture how the new believers ought to believe and behave. This was not “his opinion” which was open for discussion, something to be accepted or rejected. Paul was telling his congregation how they ought to live.
The content of Paul’s insistence is that his readers live lives worthy of God. Imagine in your mind a scale, with God’s requirements on one side and our actions on the other. “Worthy” describes the balance of those scales, something that is impossible in our own power. Paul is urging his readers to set this lofty goal of spiritual growth for themselves, that they be worthy of the one that called us.
If God is your Father, then the goal of the Christian life ought to be living in a way which makes your Father in Heaven proud to call you his child.