Q. Jesus has Peter, James, and John join Him to observe the Transfiguration. Why only these three? And, elsewhere Jesus seems to choose only certain disciples to reveal truth to and not others. So, how can we understand this? Obviously, it’s not favoritism, but maybe cliques are not all bad?
You’re right that Jesus allowed Peter, James, and John to see some parts of his ministry firsthand that the other disciples didn’t get to see. According to Mark, for example, Jesus brought only the three of them with him not just to the mountain of the Transfiguration, but also to the home of Jairus, whose daughter he raised from the dead, and apart with him in the Garden of Gethsemane. Mark also specifies that it was Peter, James, and John who asked Jesus what he meant about the temple being destroyed, prompting what is known as the Olivet Discourse (Jesus’ long teaching about the signs of the end).
You’re also right that different disciples seems to be singled out at other times for teaching and attention. According to John, for example, before Jesus fed the five thousand, he asked Philip where they could get bread to feed the large crowd. John explains that Jesus “asked this only to test him, for he already had in mind what he was going to do.” We should understand the word “test” in the sense of “challenge”; it wasn’t the case that Philip had to give a good answer or he couldn’t be a disciple any more! Rather, Jesus saw a “teachable moment” and made use of it for Philip’s advantage.
I also agree with you that this isn’t favoritism. Rather, Jesus chose to make an effective and strategic investment in specific disciples at specific times for their development as his followers and as future leaders. It’s generally accepted that someone can only have a deep influence on two or three other people at a given time. But they can have a strong influence on about a further dozen people. We see this illustrated and perhaps modeled for us in the example of Jesus.
I’m not sure I’d use the word clique, since that word tends to have a negative connotation. People in a clique are more opposed to including others than they should be. Let’s just say that Jesus shows us how to be intentional in our discipleship of others by recognizing where and how we can invest most effectively.
Good Question 
Thank you! Never heard that about a deep influence on 2-3, a strong influence on about a dz. Can I ask where did that come from? Appreciate this site.
I’ve heard the concept in a number of places. One good discussion of it is at the end of Andy Crouch’s book Culture Making, where he talks about how important it is to identify “the 3, the 12, and the 120” in your life. We all need to be a part of various “teams” of these sizes. But the smaller the number of people in the group, the more closely you will collaborate with them; you will influence them, and they will influence you.