He went on and on with his exaggerated introduction of all the members, as though he's read them from some blind date agency client file. Of course I was included in his cheesy introduction, but I'd prefer not to gloss over it here.
This doesn't seem quite right. Kyon says he'd prefer "not" to gloss over his introduction, but that's exactly what he's doing.
Hmm, I felt the same way as the original poster on this one. When I first read Kyon's statement, I thought "What, he doesn't want to gloss over his own introduction?" I think the problem is who is doing the "glossing over" that he refers to. First a bit about what "gloss" means, since it seems to have two different etymologies that have somewhat converged to mean similar things.
One etymolgy of "gloss" has it more or less synonymous with "shine" or "polish," only with a slightly negative and/or fake conotation, as something that has been "glossed" might have hidden defects underneath the shiny surface.
The other etymology comes from a literary context where to "gloss" a text is to write a brief summary in the margin of a complex text explaining an equation or a phrase in another language. This also has a slightly negative equation, as the summary may miss some key points of the original version.
The idom "gloss over" comes to some extent from both of the the two etymologies but it focuses especially on the negative connotations that each has. It means to cover up, give little detail, or to skimp.
Clearly Kyon feels that Koizumi's introductions of the other members of SOS-dan are rather simplified and overly favorable ("glossed over" as it were), but then he himself "glosses over" what is said about him (by not quoting it).
Maybe "gloss" is not the right word, but ultimately, Kyon's reluctance to quote Koizumi's introduction of him means we still don't know Kyon's real name.