i think he hates that wenger is respected and placed in the same tier as him. mourinho can point to his trophy cabinet over the last 9 yrs, managing for owners with the highest of expectations, and when he sees wenger free to do as he pleases and use the club as a kindergarten when he wanted, with no repercussions for failure, i think it pisses him off.
it wouldn't surprise me if deep down, he wanted the arsenal job. total control, no pressure or interference from the board - it must be pretty draining having to work for chelsea, madrid, inter, etc.