There may be other reasons, too, but in this instance it should be because he's the son of the previous emperor. Since Caitel is the emperor, things could become fraught if a powerful rival imperial branch developed - as it was in the past when there were many children/siblings with a claim to imperial power.
Asisi is Caitel half brother? Because from what I understand is Asisi was already born when his mother started having a affair with the previous emperor so that may be the reason why Asisi dad abuse him to cope with the cheating as he couldn’t touch the emperor and Caitel killed all his siblings except for the runaway 6th prince and knowing him it wouldn’t matter if Asisi and him grew up together he would still kill him back then if they were really blood related. But i guess you could be also right them being siblings as Asisi dad called him a ‘curse’ it might be because he is the result of the affair and abuse him because he isn’t his real child.
Actually, if I remember correctly, the previous Emperor was one of his brothers, so in fact he would be Caitel's nephew (or half-nephew, if their mothers were different?) and Ria's cousin. Their actual ages are unclear, so, even though he and Caitel seem more in the same generation because they were adults when Ria was a child, I don't think there's anything in the story so far that would preclude them having something like a 5 or 10-year age gap?
But, I just went back to check what they actually said, and you're right that they didn't actually state that he was the Emperor's son, only Lady Cecilia's son. I assumed that meant he must be the Emperor's son. I thought it was clearly implied, since I didn't think she would have had so much power as a mistress if she hadn't exclusively been only in a relationship with him. If she had a son already with someone else (or been married), I had assumed she wouldn't have had as much influence over the Emperor and the court. It doesn't actually state that, though, so I realise now that I might have been over-inferring. It is just a possibility but not the only one.
Can anyone tell me why asisi cant get married??