No, I am not going to quote TW lore because A) I do not know it so I'd just have to go off the wiki and B) it is one of the farthest things from quest canon.
As for why their mythology might want to paint magic as evil unless X either out of draconic design or simple cultural evolution it is because it is. All other things being equal it is better in warhammer not to interact with strange magic. The average human does not have the knowledge, the skills or even the senses to protect themselves effectively from a magician wishing them harm or not in proper control of them power.
Then why are you arguing that Cathayans are magophobic if you aren't going to draw upon what lore about them exists? Do you see the flaw here? Do you not see the problem in arguing that a society you aren't familiar with
must be magophobic because the society you are familiar with is? Furthermore, Total Warhammer lore is just about the only lore on Cathay we have, as it Cathay is extensively covered nowhere else. Boney has mentioned that Games Workshop's Cathay will be drawn upon if we ever visit.
The problem with this is that you are starting from a prior that the Empire is normal and that all people across the world act like peasants do in the Empire and are working backwards to justify it. You need to start with the conditions that Cathay is in and work
forwards to figure out what their opinion of magic would be. They are entirely ruled by wizards, those wizards would certainly want magic-capable Cathayans to be harnessed rather than killed, those wizards are basically worshiped, those wizards have extensively shaped Cathayan society to suit them. Why would these people treat magic the same way that peasants in the Empire do?
The average human also does not possess the knowledge, skills, or anything to protect themselves from abuse by nobility. Are you going to argue that all humans in-setting are noble-phobic? Mind you, hating the nobility is infinitely more justifiable than hating magic users.
Honest to god, I'm pretty sure we have no idea.
It's stated that the Emperor and Empress had 9 children, but there hasn't even been a hint of a mention of the last 2. No 'some disappeared in ancient days' or anything like that.
Obviously we don't have a full Cathay army book or anything, but the absence has been glaring.
The impression I got is that Games Workshop had intended them to be three Lost
Primarchs Dragons, but Creative Assembly convinced them to let them have one of them to serve as
Princess Peach the campaign objective. The Old World gives us insight into what Cathay was like during
2076 2276 IC and there were only the five dragon children. I am pretty confident they all were lost before -1800 IC, when the Emperor built the Bastion, divied up the lands, and retreated to Weijin.