Most of us have heard these words in the trailer spoken by Pike, presumably to Kirk:
"There's greatness in you, but there's not an ounce of humility"
As has already been speculated by others, this line of dialogue may be a launching point of sorts for Kirk's personal growth and journey through this film -- his attempt to gain the humility Pike says Kirk is lacking.
Also, as others have speculated, I think that Pike may die in this film, and those may be among the last words that Pike speaks to Kirk. If that is so, Kirk may have even a greater reason to take Pike's words to heart (to honor Pike in death, so-to-speak).
...But to further expand on this idea:
Pike goes on to say:
"You think you can't make mistakes, but there's going to come a moment when you realize you're wrong about that. And you're going to get yourself and everyone under your command killed."
Does anyone think that if Pike does die, that perhaps Kirk did something (out out hubris/cockiness/lack of humility) that he feels may have LEAD TO
Pike's death? I'm not saying Kirk's actions would necessarily be directly
responsible for Pike's death, but maybe Kirk feels he may have done something out of arrogance that eventually lead to Pike's death...
...something that Kirk feels if he did differently (i.e., if he had acted with greater humility and less cockiness), then Pike possibly would not have gotten killed.
In that respect, if Pike dies in this film, maybe his death will become a huge part of Kirk's personal journey and personal growth in this film.