What if Yuri Egin was actually a clone of Egyn (King of Water)?
I gathered a couple thoughts starting from this:

I don't know much about japanese language, but I combined my little knowledge I have of it with some net research and came up with this:
the name "Rin" can be written in different kanji (pardon my ignorance, but this is what I read on Wikipedia): such as 倫, 凛, 臨, 琳, 燐, りん in hiragana or リン in katakana. Probably Kato's choice for our Rin's is just random, but the one she used is this: 燐. Which it should mean: phosphorus. Now, phosphorus is a chemical element. Some of its main applications are related to fire-stuff (fireworks, matches...).
On the other hand, "Yukio" (random note, take a look at this page, I found it quite interesting
The Meaning of the name Yukio) is written with this kanji: 雪男. And it essentially means: man of the snow. Something snow related... water related.
Ok, Rin and Yukio are two very different brothers. Can we consider "opposite" an even more suitable definition? If that's the case, aren't fire and water two opposite elements for definition as well?
Now, name aspect aside. There's this one thing that suddenly crossed my mind: what if Yuri Egin is actually a clone of the King of Water? For all we know, prolly both Rin and Yukio actually inherited the Satan's blue flames power gene but Rin got it as his dominant one and Yukio as his recessive one. But what if Yukio's dominant gene is related to the possible water element of his mother? I thought of something stupid, such as the water element suppressing the "fire" element of the flames. And this as a possible explanation for why Yukio can't access his Satan's blue flames power gene.
I have a couple considerations about Yukio having some "water related potential" in him. Such as the fact he can summon Naiads (kin of the King of Water) even w/out possessing a Tamer Meister. Also, maybe it got nothing to do with this matter, but if you consider the fact that the Kraken is also kin of the King of Water, I have this lil theory in my mind that the reason it suddenly made his appearance right after the Kyoto adventure may have an explanation. Yukio had just awoke the power in his eyes (or whatever), so he had kinda just awaken his demonic side as well. What if the Kraken "sensed" it (the awakening of the "aura" of the King of Water within Yukio's genes) and reacted to this event?
Also, Lucifer stated that HE has the power to unlock Yukio's real potential. Well, Egyn is part of the anti-human faction just as Lucifer. So he's essentially Lucifer's ally.
What do you think about this?