Re: Why did Spock show emotion around Pike?
Possible In-universe explanation: when we see Spock serving with Pike, he is younger and more inexperienced than when we see the more reserved Spock of the Kirk era. The younger Spock was perhaps overcompanstating a bit, trying to find a way to fit in better with all the emotional humans he was stuck hanging around with. We see much the same sort of behavior with Saavik in STII later on (though by the time we see her in STIII, she's apparantly decided to exercise a lot more self-control in public).
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