I don't reject your interpretation. However, I do set it next to several caveats.
First and foremost, the author generally steers all the characters away from commenting on, much less prying into, their personal lives. The main point being to keep the stage uncluttered. It's not an iron rule, but even oblique references to parents, individual teachers, etc. are kept to a minimum.
Beyond this general consideration, valid for all characters, Kyon is himself a polite, considerate person, respectful of personal boundaries. Shamisen, an actual tomcat, prefers to hang wih him. I can't reference the exact words, but Ben Franklin once observed that, " a man who can make friends with strange cats will have good fortune in life." Nagato, the strangest cat of all, is his friend. The sensitivity, appreciation of nuance and reflexive respect for the boundaries of others, these are qualities that bring a man good fortune due to how they temper his interactions with other men. The cat thing is just a flag.
Kyon's edginess with Koizumi is connected to Koizumi not being accessible for friendship. This is my view. Kyon isn't himself a mere tomcat, incapable of tolerating other males, the problem isn't that simple.
Earlier in the same scene, Kyon feels some jealousy about Koizumi touching Mikuru. On a tomcat level, Kyon recognizes Koizumi as a rival, quite possibly "better" than him on that level. I think the jealousy regarding Mikuru is a cover for deeper insecurity about Haruhi. What stops Koizumi from taking her? Koizumi's hypothetical tomcat boyfriend? Really?
Finally I reflect back on this earlier scene:
I stared at the sleeping face of Shamisen who had wrapped himself in a bundle on my bed, while indulging in a sense of warmth. While wondering deeply where that warm feeling came from, I might as well try and figure out where the division between love and lust begins and ends. At that moment a thought sparked in my head that cried out That's it!...
Kyon doesn't hold lust cut off from love in high regard.
This is all just interesting stuff to consider.
Nutcase