Interesting things happen when you confine your study of “teaching” (διδάσκω) to Matthew. Jesus has a three-fold ministry of preaching, teaching and healing. He involves the 12 in preaching and healing in Matthew 10, when he sends them out two by two. But only Jesus teaches in the first gospel. Matthew 28:20 is the first time (in the first gospel) where the disciples are included in teaching. Even then what they teach is restricted to teach the disciples they make to obey all of Jesus’ commands.
My study of Matthew leads me to the conviction that Jesus is the only teacher for disciples. As sent out disciple makers we are to point others to Jesus. What we teach them is to obey Jesus’ teaching. It is Jesus who defines what disciple making looks like by the way he makes disciples. His disciples are contrasted with those of John the Baptist and the disciples of the religious leaders. The disciples at the heart of the first gospel are people who have responded to Jesus’ call to follow. It is at its basic core a submissive relationship with the Son of God. Jesus provides the content for all his disciples.
You don’t get this nuanced perspective from the other biblical authors, but only Matthew uses that phrase “make disciples.” We need to be sure we use that phrase in ways consistent with what he reveals about what that entails. Don’t begin by going to Luke-Acts, Mark or John.
I originally posted most of the preceding comments in a discussion area considering the question, “How are we to define the word ‘teaching’ in the Great Commission?” The query sparked much dialogue. My desire was to answer the question by looking to the context where the word “teach” appears. The immediate context of the last four verses is significant, but it is inadequate to know how the term is used by the first evangelist. You only get that from what Jesus has already said and revealed through his actions about the nature of disciple making