The translation could be better, because literally the Greek is ‘make disciples’, and it's somewhat terse to say ‘teach’. By using the word ‘teach’ our King James translators have unwittingly concealed the fact that this first ‘teach’ is about soul winning.
They have to be made disciples, before you baptize them; they have to be converted. They have to be presented with, and persuaded by the saving gospel of Christ, the good news. They must have come to him and repented and trusted him and found him, and then they can be baptized: the one precedes the other.
‘Baptizing them’ – that is a transliteration from the Greek. The translators have hesitated to translate it because it is too controversial, but literally the Greek word means ‘dip’. ‘Dipping them in the name of the Father, and of the Son, and of the Holy Ghost.’ The person was plunged into the water to symbolise death to the old life, and came up out of the water to symbolise rising to a new life. So it's not only washing that is represented; it's death and resurrection.
‘Baptizing them in the name of the Father, and of the Son, and of the Holy Ghost.’ These words are important. We could translate this: ‘Baptizing them [into] the name of the Father, and of the Son, and of the Holy Ghost.’ Elsewhere in the New Testament the very same word is translated in that way. What is the difference between being baptized in the name of God, and into the name of God? It is easy to understand. If I do something ‘in the name of God’, it means I do it by his authority, but if I do something ‘into the name of God’, it means I come into the experience that he gives: into his power, into his life, into his service. If I am baptized ‘in the name’ of Father, Son, and Holy Spirit, I’m baptized by his authority; but if I am baptized ‘into the name’, I’m baptized into an experience of Christ and of the Father and of the Holy Spirit. That is why we must be careful with the word when administering baptism.
Why are all three members of the Godhead named? Because if you’re baptized into the name of the Son he is the Saviour. You’re baptized into him, a believer in him, in his atoning death, in his salvation. He has purchased it for you. He has given you the new life. If you're baptized into the name of the Father, then you’re a member of the divine family, the divine household, the roll of the citizens of heaven, the people whose names are in the Lamb's book of life. You’re not like the Father; you’re not like God; but you are admitted into the household of God's people. If you’re baptized into the name of the Holy Spirit he has come to you. In a mysterious, inexplicable way, he is resident in you to enliven your conscience, to encourage you, to warn you, to help you. He yearns jealously for you, the Scripture says, to keep you on the side of the Lord and to keep you from the evil one. So every word of it is precious to the believer.
Some who wish to justify the baptizing of infants don’t seem to notice that we read ‘make disciples’ before he read ‘baptizing them’. That is why we call it believers’ baptism, not infant baptism. Baptism is just a symbol of what has happened to you. You come to the Lord, and you say in your baptism: ‘I'm dead to the old life and I've risen to a new life.’ Furthermore they go to Acts 2. The apostle Peter has been preaching on the day of Pentecost, and he has commanded the people: ‘Repent, and be baptized every one of you in the name of Jesus Christ for the remission of sins, and ye shall receive the gift of the Holy Ghost’ (Acts 2:38). Then he says, ‘For the promise is unto you, and to your children’ (Acts 2:39). ‘There you are’, they say, ‘so we should baptize the children.’ But they don’t read on: ‘even [to] as many as the Lord our God shall call’ (Acts 2:39). They have to be called and saved in order to be baptized. A little later, it says, ‘Then they who received his word were baptized.’ All the way through the Scripture, salvation comes before baptism, and baptism is treated as the sign of what has already happened, and of the pledge to God that you make.