I'd say it is a mix of two things:
(1) Dwight definitely stepped on Shaq's toes. Being the new face of the Orlando Magic (like Shaq was), taking the same "Superman" nickname (like Shaq), wearing the cape in the dunk contest. Each touching to close to home for Shaq.
There was an anger that Dwight did not create a personality / identity of his own and instead was just trying to steal Shaq's. To take what Shaq had built. Both in terms of the NBA overall and also in Orlando where Shaq still has big emotional ties to.
It was disrespect - at least to Shaq.
(2) I reckon Shaq genuinely believes Dwight is over-rated. You can see in his commentary as well as his own style of play that Shaq views scoring and being the go-to scorer as the most important and only real way for a franchise player to be. Dwight was a good but unexceptional scorer.
I also believe Shaq's matchups with Dwight played a role here as well. Shaq was able to defend and shut-down Dwight's scoring comfortably. Dwight was essentially Shaq but 3-4 inches shorter and 40-60lbs lighter. Shaq was able to shut down Dwight's power game in the post easily and Dwight lacked the counters to cause Shaq much trouble. In contast, guys like Ewing, D-Robinson, Hakeem, Mourning gave Shaq much more trouble.
... and these matchups with Dwight were in Shaq's elder years when he was no longer the force he once was. Imagine how much old Shaq would have struggled with those centers of the 90s in their prime. Now compare that to how comfortably Shaq could handle Dwight as an old man.
I believe Shaq regards Dwight closer to a Dikembe Mutombo because of his lack of go-to scoring ability than he does guys like Alonzo, Hakeem, D-Rob or Ewing. And that just comes down to how Shaq views the game of basketball and what the duties are of a franchise player -- to be the go-to scorer. To score 25-30ppg. To have the offense run through you in the post.
And I reckon Shaq rates Mutombo above Dwight because Mutombo maintained his standards for longer while Dwight dropped off year-by-year after leaving Orlando. A short peak for Dwight [Mutombo level) and not enough longevity at a high level (below Mutombo). This is how I believe Shaq rates Dwight given Shaq's views on the game.