sos brigade wannabe

yuki can say whatever she wants

I think before Haruhi, Kyon kind of sucked at maintaining connections that would actually last him multiple lifetimes. His friendships up until this point had been surface level, and nothing that he could truly call family. As a result, he feels a certain possessiveness over all members of the SOS-Brigade, including Koizumi, while also being absolutely offended at their suspicions that Kyon seems like he'd be calmer and happier without them. That rough over-dramatic outer shell he wears at every moment houses a deeply empathetic heart with seemingly endless love and protection to give for the ones he truly cherishes. 

Koizumi likes to play with that outer shell, genuinely fascinated by it, and it annoys the hell out of Kyon. It disrupts his trusted system of vetting the true loved ones he chooses to protect. With Koizumi, Kyon's engaging with a level of genuine curiosity he has no true experience in, and repels it at every turn to satisfy his firing alarm bells, the ones that tell him that an intruder is attempting to infiltrate for reasons of mal-intent. Koizumi being another guy is of course an unfortunate crucial trigger to that alarm, and I think that itself reveals more about Kyon's overall internal struggle.

Despite finding his truest family in the SOS-Brigade, he has yet to fully disown the superficial life and relationships that had come before it. He stays tethered to the rules and regulations of the tangible world around him. For all its benefits, critical flaws, and obvious blindspots, it had once promised security for a child who felt he had no choice but to accept the world in front of him, lest he find himself abandoned by it.