Early in Star Trek 3, this enlightening conversation occurs:
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In this scene, Admiral Kirk pleads with Starfleet's top administrator to be allowed to return Spock to Vulcan. Notice that it is emphasized that Kirk is thought of as an exemplary Star Fleet officer (NOT a hothead, nor a rebel). Up to this point in Kirk's career, his record is apparently unstained. He is also apparently liked as a person by this superior officer.
In the first part of the conversation (seen here), Kirk explains that he takes responsibility for Spock's soul, as if it were his own. This admission, and with it the implied depth and breath of Kirk's intimacy with Spock, stuns the other man into silence.
