‘Whom we proclaim, admonishing every man, and teaching every man in all wisdom, that we may present every man perfect in Christ.'
Christ's work of perfecting His people is largely carried out through the ministry of the word. So here Paul refers to such work carried out by himself and his fellow-workers. Firstly they proclaim Christ (‘Whom we proclaim'). Then they admonish and teach ‘in all wisdom', in the only wisdom, in the totality of the wisdom, that comes from the word of God, about the cross which to the Christian is true wisdom (1 Corinthians 1:18 with 24), about Christ Who is the Wisdom from God (1 Corinthians 1:30), and ‘in Whom are hidden all the treasures of wisdom and knowledge' (Colossians 2:3).
And their aim? To present every man perfect and complete in Christ, which parallels, of course, the aim of Christ Himself. Paul's eyes are here on the second coming of Christ (His parousia - see 1 Thessalonians 4:15-17). Indeed he prays for the Thessalonians that ‘the God of peace' will Himself sanctify them wholly and that their whole spirit, soul and body may be preserved complete and blameless ‘at the coming of our Lord Jesus Christ' (1 Thessalonians 5:23). For ‘we shall be like Him, for we shall see Him as He is' (1 John 3:2).
‘Admonishing every man and teaching every man.' Two necessary sides to the same responsibility, the stick and the carrot. Admonishment (‘admonishing, warning') without teaching is harsh and unsustainable, teaching without admonishment can produce educated potatoes. Notice the double emphasis on ‘every man'. This is to be for all, not just the chosen few.