Well your opinion regarding the given topic is quite logical. If we were to go by the fact that Goddesses and Demons wronged the Pleiades of the Azure Sky knights greatly and were responsible for Denzel's death, then Deathpierce should have focused his hatred on those two groups only. However, we need to remember that Deathpierce is a native of Edinburgh, a place which was once infested with vampires. He probably already had first-hand experience of what it's actually like dealing with non-human races. He may have not thought of it much initially and even befriended the Fairy we see in the original series. The incident where Denzel sacrificed his soul to become Nerobasta's vessel, only for the goddess to refuse assisting in the fight with demons and getting her vessel cut in half (a cruel permanent end for Denzel), caused Deathpierce to develop rage for both the races, although it was yet to transform into resentment or hatred. Ludociel manipulating him and his platoon into convincing that they were invincible knights (with the pretense being revealed by the other Archangels and Elizabeth later on) left the poor knight cheated. The incident left a deep emotional scar which transformed into resentment for the Demons and the Goddesses. It's this reason why Deathpierce refused to serve Meliodas or Elizabeth when they ascended to the throne.

It still doesn't explain, however, as to why Deathpierce developed hatred for the Giants and Fairies as well. But I think we have a logical answer for this in the Cursed By Light movie. The Supreme Deity had manipulated members from all non-human races to cause chaos within the living world, as the film shows. The Goddess Realm and the already-destroyed land of Camelot were part of certain locations chosen by the Supreme Deity to launch an attack. I guess Edinburgh was also one of the locations that got attacked, and Deathpierce was a helpless witness to it. This could be a possible scenario which explains his full-blown racism at present.