'Stuck on himself'

Are you talking about someone in particular?

I got it from story books very often. It is always the case the girls are drooling over a guy but he doesn't give them a glance or anything

What dictionaries do you use, whl?

The reason could be either that this expression is quite a new one and didn't find its way yet into the dictionaries or that this expression has not been standardized (yet).

In the latter case, this is mainly true for those dictionaries which are regarded to be a guideline (e.g. Oxford dictionaries for BE or "Webster" for AE - those would on

Longman, Oxford, Heritage and Cambridge. They all fail me on this phrase, Pem

Strange indeed...
I'm going to look it up later on in my "Hornby", "Langenscheidt", and "Pons" dictionaries. Those are a few years old already, but maybe I will find something

The only similar meaning I have found is stuck with; I know you might think this is stupid but we are stuck with each other, aren't we?

whl, I looked it up in all the three dictionaries, I mentioned:

Hornby's "Oxford Advanced Learner's Dictionary" (edition of 1963) which is published by Oxford university press, and my Langenscheidt's pocket dictionary (1982) don't have any entries for "stuck on".

But I could find an entry for 'stuck-up' in my "Pons English Learner's dictionary" from 1996:

--> "'st

Well, I use dictionaries from the CD and the internet. So they must be the most up-to-date. Pem.

Also "LEO" (a German-English online dictionary) knows "stuck-up" meaning "arrogant, snooty".
The only translation it gives for "stuck on" is "glued to, affixed".

I have never heard 'stuck on' used that way. It would usually mean fixated, or prevented from progressing.
Stuck-up is quite similar to 'snobby' or 'snobbish', and would seem to fit your context.